Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
23101	Simplify/Condense	2 natural log of x+1-3 natural log of x+5	$2 \ln (x + 1) - 3 \ln (x + 5)$
23102	Simplify/Condense	2 natural log of x+3+3 natural log of x-2	$2 \ln (x + 3) + 3 \ln (x - 2)$
23103	Simplify/Condense	2 natural log of x+3-6 natural log of x	$2 \ln (x + 3) - 6 \ln (x)$
23104	Simplify/Condense	2 natural log of x+3 natural log of z-(4 natural log of y+5 natural log of x)	$2 \ln (x) + 3 \ln (z) - (4 \ln (y) + 5 \ln (x))$
23105	Simplify/Condense	2 natural log of x+4 natural log of y- natural log of 5	$2 \ln (x) + 4 \ln (y) - \ln (5)$
23106	Simplify/Condense	2 natural log of x+ natural log of square root of x^2-1-1/2* natural log of x-1	$2 \ln (x) + \ln (\sqrt{x^{2} - 1}) - \frac{1}{2} \cdot \ln (x - 1)$
23107	Simplify/Condense	2 natural log of x-3 natural log of x-4+1/2* natural log of x+5	$2 \ln (x) - 3 \ln (x - 4) + \frac{1}{2} \cdot \ln (x + 5)$
23108	Simplify/Condense	2 natural log of x-1/3* natural log of x+1	$2 \ln (x) - \frac{1}{3} \cdot \ln (x + 1)$
23109	Simplify/Condense	2 natural log of 3x-1+ natural log of 5- natural log of x	$2 \ln (3 x - 1) + \ln (5) - \ln (x)$
23110	Simplify/Condense	2 natural log of square root of x+2 natural log of x	$2 \ln (\sqrt{x}) + 2 \ln (x)$
23111	Simplify/Condense	2 natural log of square root of x+3 natural log of 2x	$2 \ln (\sqrt{x}) + 3 \ln (2 x)$
23112	Simplify/Condense	2 log of A-1/2* log of N	$2 \log (A) - \frac{1}{2} \cdot \log (N)$
23113	Simplify/Condense	2 log of a-3 log of b+ log of c-4 log of d	$2 \log (a) - 3 \log (b) + \log (c) - 4 \log (d)$
23114	Simplify/Condense	2 log of u+3 log of w-6 log of v	$2 \log (u) + 3 \log (w) - 6 \log (v)$
23115	Simplify/Condense	2 log of x	$2 \log (x)$
23116	Simplify/Condense	2 log of x-( log of y- log of z)	$2 \log (x) - (\log (y) - \log (z))$
23117	Simplify/Condense	2 log of x-1/4* log of x^2+1+5 log of x-1	$2 \log (x) - \frac{1}{4} \cdot \log (x^{2} + 1) + 5 \log (x - 1)$
23118	Simplify/Condense	2 log of x-1/5* log of x^2+1+3 log of x-1	$2 \log (x) - \frac{1}{5} \cdot \log (x^{2} + 1) + 3 \log (x - 1)$
23119	Simplify/Condense	2 log of 33- log of 3	$2 \log (33) - \log (3)$
23120	Simplify/Condense	2 log of 4- log of 3+2 log of x-4	$2 \log (4) - \log (3) + 2 \log (x) - 4$
23121	Simplify/Condense	2 log of 5-1/2* log of 7- log of 3.8	$2 \log (5) - \frac{1}{2} \cdot \log (7) - \log (3.8)$
23122	Simplify/Condense	2 log of 5+3 log of 4-4 log of 2	$2 \log (5) + 3 \log (4) - 4 \log (2)$
23123	Simplify/Condense	2 log of 5x+ log of 5x^2-10 log of 5*5- log of 5x^7	$2 \log (5) x + \log (5) x^{2} - 10 \log (5) \cdot 5 - \log (5) x^{7}$
23124	Simplify/Condense	2 log of 5x^3-1/2* log of 2x+3	$2 \log (5 x^{3}) - \frac{1}{2} \cdot \log (2 x + 3)$
23125	Simplify/Condense	2 log of x^6y^2+5 log of 1/x-2 log of y	$2 \log (x^{6} y^{2}) + 5 \log (\frac{1}{x}) - 2 \log (y)$
23126	Simplify/Condense	2 log of 1	$2 \log (1)$
23127	Simplify/Condense	2 log of 10- log of 11	$2 \log (10) - \log (11)$
23128	Simplify/Condense	2 log of 100- log of 1000	$2 \log (100) - \log (1000)$
23129	Simplify/Condense	2 log of 12+2 log of 8-2 log of 3	$2 \log (12) + 2 \log (8) - 2 \log (3)$
23130	Simplify/Condense	2 log of 12-3 log of 25	$2 \log (12) - 3 \log (25)$
23131	Simplify/Condense	2 log of 2+3 log of x-1/2*( log of x+3+ log of x-2)	$2 \log (2) + 3 \log (x) - \frac{1}{2} \cdot (\log (x + 3) + \log (x - 2))$
23132	Simplify/Condense	2 log of 2x- log of y- log of 3+2 log of 5	$2 \log (2 x) - \log (y) - \log (3 + 2) \log (5)$
23133	Simplify/Condense	2 log of 3+3 log of 2	$2 \log (3) + 3 \log (2)$
23134	Simplify/Condense	2 log of 3+ log of 5	$2 \log (3) + \log (5)$
23135	Simplify/Condense	-2 log of square root of y+5/2* log of 9x^4+1/2* log of 2 square root of x	$- 2 \log (\sqrt{y}) + \frac{5}{2} \cdot \log (9 x^{4}) + \frac{1}{2} \cdot \log (2 \sqrt{x})$
23136	Simplify/Condense	2 log of x^3y^5+3 log of 1/x-4 log of y	$2 \log (x^{3} y^{5}) + 3 \log (\frac{1}{x}) - 4 \log (y)$
23137	Simplify/Condense	2 natural log of x-3 natural log of y-4 natural log of z	$2 \ln (x) - 3 \ln (y) - 4 \ln (z)$
23138	Simplify/Condense	3 log base 2 of x-1+ log base 2 of 4=5	$3 \log_{2} (x - 1) + \log_{2} (4) = 5$
23139	Simplify/Condense	3 log base 3 of 2+ log base 3 of 5- log base 3 of 10	$3 \log_{3} (2) + \log_{3} (5) - \log_{3} (10)$
23140	Simplify/Condense	3 log base 3 of 27+9 log base 3 of x-3 log base 3 of 729	$3 \log_{3} (27) + 9 \log_{3} (x) - 3 \log_{3} (729)$
23141	Simplify/Condense	3 log base 3 of 3	$3 \log_{3} (3)$
23142	Simplify/Condense	3 log base 3 of 3-3/4* log base 3 of 81+1/3* log base 3 of 1/27	$3 \log_{3} (3) - \frac{3}{4} \cdot \log_{3} (81) + \frac{1}{3} \cdot \log_{3} (\frac{1}{27})$
23143	Simplify/Condense	3 log base 2 of -2	$3 \log_{2} (- 2)$
23144	Simplify/Condense	3 log base 2 of 4+4 log base 2 of 1/16-2 log base 2 of 2+ log base 2 of 1	$3 \log_{2} (4) + 4 \log_{2} (\frac{1}{16}) - 2 \log_{2} (2) + \log_{2} (1)$
23145	Simplify/Condense	3 log base 2 of 5- log base 2 of x	$3 \log_{2} (5) - \log_{2} (x)$
23146	Simplify/Condense	3 log of x+2 log of x-3	$3 \log (x) + 2 \log (x - 3)$
23147	Simplify/Condense	3 log of x+6 log of x+7	$3 \log (x) + 6 \log (x + 7)$
23148	Simplify/Condense	3 log of x-2 log of x+2	$3 \log (x) - 2 \log (x + 2)$
23149	Simplify/Condense	3 log base 16 of 2+ log base 16 of 2	$3 \log_{16} (2) + \log_{16} (2)$
23150	Simplify/Condense	3 natural log of x-3 natural log of y	$3 \ln (x) - 3 \ln (y)$
23151	Simplify/Condense	3( log base 5 of x+3 log base 5 of y-4 log base 5 of z)	$3 (\log_{5} (x) + 3 \log_{5} (y) - 4 \log_{5} (z))$
23152	Simplify/Condense	3( log base 7 of x+3 log base 7 of y-f log base 7 of z)	$3 (\log_{7} (x) + 3 \log_{7} (y) - f \log_{7} (z))$
23153	Simplify/Condense	3(4)+100 log of 4	$3 (4) + 100 \log (4)$
23154	Simplify/Condense	3( natural log of 3- natural log of x)+( natural log of x- natural log of 9)	$3 (\ln (3 - \ln (x))) + (\ln (x) - \ln (9))$
23155	Simplify/Condense	3( log of a+ log of B)- log of c-2	$3 (\log (a) + \log (B)) - \log (c) - 2$
23156	Simplify/Condense	3* log base 2 of 10	$3 \cdot \log_{2} (10)$
23157	Simplify/Condense	3* natural log of x^3y+2 natural log of y*z^2	$3 \cdot \ln (x^{3} \cdot y) + 2 \cdot \ln (y \cdot z^{2})$
23158	Simplify/Condense	3* log of 2	$3 \cdot \log (2)$
23159	Simplify/Condense	3* log of 4	$3 \cdot \log (4)$
23160	Simplify/Condense	3( natural log of x+2 natural log of x+2)-1/2* natural log of x-1	$3 (\ln (x) + 2 \ln (x + 2)) - \frac{1}{2} \cdot \ln (x - 1)$
23161	Simplify/Condense	3( natural log of x-2 natural log of x^2+1)+2 natural log of 5	$3 (\ln (x) - 2 \ln (x^{2} + 1)) + 2 \ln (5)$
23162	Simplify/Condense	3( natural log of z+ natural log of z+1)-5 natural log of z-7	$3 (\ln (z) + \ln (z + 1)) - 5 \ln (z - 7)$
23163	Simplify/Condense	3( natural log of z+ natural log of z+9)-2 natural log of z-4	$3 (\ln (z) + \ln (z + 9)) - 2 \ln (z - 4)$
23164	Simplify/Condense	3 log of (3)^12	$3 \log ({(3)}^{12})$
23165	Simplify/Condense	3 log of (3)^(3 square root of 243)	$3 \log ({(3)}^{3 \sqrt{243}})$
23166	Simplify/Condense	3 log of (3)^5- log of (3)^4	$3 \log ({(3)}^{5}) - \log ({(3)}^{4})$
23167	Simplify/Condense	3 log base 0.13 of 2+ log base 0.13 of 7	$3 \log_{0.13} (2) + \log_{0.13} (7)$
23168	Simplify/Condense	2x log of 3-x log of 3	$2 x \log (3) - x \log (3)$
23169	Simplify/Condense	2x log of 7-5x log of 3	$2 x \log (7) - 5 x \log (3)$
23170	Simplify/Condense	3 log base 2 of x+6 log base 7 of y-8 log base 7 of z	$3 \log_{2} (x) + 6 \log_{7} (y) - 8 \log_{7} (z)$
23171	Simplify/Condense	2 log of x+1/3* log of y-6 log of z	$2 \log (x) + \frac{1}{3} \cdot \log (y) - 6 \log (z)$
23172	Simplify/Condense	2 log of x+3 log of y-4 log of z	$2 \log (x) + 3 \log (y) - 4 \log (z)$
23173	Simplify/Condense	2 log of x-1+1/5* log of x-2-7 log of x+2- log of 2x-1	$2 \log (x - 1) + \frac{1}{5} \cdot \log (x - 2) - 7 \log (x + 2) - \log (2 x - 1)$
23174	Simplify/Condense	2 log of x-2+3 log of y+6 log of z-5 log of x	$2 \log (x - 2) + 3 \log (y) + 6 \log (z) - 5 \log (x)$
23175	Simplify/Condense	2 log of x-3 log of x-4	$2 \log (x - 3) \log (x - 4)$
23176	Simplify/Condense	-2 log of x-5 log of x+6	$- 2 \log (x - 5) \log (x + 6)$
23177	Simplify/Condense	2 log of z+1+ log of 3z+6	$2 \log (z + 1) + \log (3 z + 6)$
23178	Simplify/Condense	2x square root of x-2+ natural log of x	$2 x \sqrt{x} - 2 + \ln (x)$
23179	Simplify/Condense	2x-1 log base 2 of 3-3	$2 x - 1 \log_{2} (3) - 3$
23180	Simplify/Condense	2x natural log of 1/x-x	$2 x \ln (\frac{1}{x}) - x$
23181	Simplify/Condense	2 log of x+6 log of y	$2 \log (x) + 6 \log (y)$
23182	Simplify/Condense	2 log of x+ log of x-1-1/2* log of x^2+1	$2 \log (x) + \log (x - 1) - \frac{1}{2} \cdot \log (x^{2} + 1)$
23183	Simplify/Condense	2 log of x-2 log of x+1	$2 \log (x) - 2 \log (x + 1)$
23184	Simplify/Condense	2 log of x-3 log of x^2+1+5 log of x-1	$2 \log (x) - 3 \log (x^{2} + 1) + 5 \log (x - 1)$
23185	Simplify/Condense	2 log of x-3 log of y+4 log of z-5 log of w	$2 \log (x) - 3 \log (y) + 4 \log (z) - 5 \log (w)$
23186	Simplify/Condense	-2 log of x-3 log of y+ log of z	$- 2 \log (x) - 3 \log (y) + \log (z)$
23187	Simplify/Condense	2 log of x- log of y+3 log of 2	$2 \log (x) - \log (y) + 3 \log (2)$
23188	Simplify/Condense	2 log of x- log of y+3 log of z	$2 \log (x) - \log (y) + 3 \log (z)$
23189	Simplify/Condense	2 log of x+3-3 log of x-7+5 log of x-2- log of (x)^2	$2 \log (x + 3) - 3 \log (x - 7) + 5 \log (x - 2) - \log ({(x)}^{2})$
23190	Simplify/Condense	2 log of x+3-3 log of x-7+5 log of x-2- log of x^2	$2 \log (x + 3) - 3 \log (x - 7) + 5 \log (x - 2) - \log (x^{2})$
23191	Simplify/Condense	log base 4 of 16+ log base 4 of 3x+2y	$\log_{4} (16) + \log_{4} (3 x + 2 y)$
23192	Simplify/Condense	log base 4 of 16+ log base 4 of 4	$\log_{4} (16) + \log_{4} (4)$
23193	Simplify/Condense	log base 4 of 16x^3	$\log_{4} (16 x^{3})$
23194	Simplify/Condense	log base 4 of 16x+64y	$\log_{4} (16 x + 64 y)$
23195	Simplify/Condense	log base 4 of 18- log base 4 of 19	$\log_{4} (18) - \log_{4} (19)$
23196	Simplify/Condense	log base 4 of 129- log base 4 of 3	$\log_{4} (129) - \log_{4} (3)$
23197	Simplify/Condense	log base 4 of 13+5 log base 4 of 3	$\log_{4} (13) + 5 \log_{4} (3)$
23198	Simplify/Condense	log base 4 of 15	$\log_{4} (15)$
23199	Simplify/Condense	log base 4 of x^2+14x+49- log base 4 of x+7	$\log_{4} (x^{2} + 14 x + 49) - \log_{4} (x + 7)$
23200	Simplify/Condense	log base 4 of x^2+18x+65- log base 4 of x+13	$\log_{4} (x^{2} + 18 x + 65) - \log_{4} (x + 13)$