Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40301	Simplify/Condense	log base p of 203	$\log_{p} (203)$
40302	Simplify/Condense	log base 729 of 729+ log base 27 of 729+ log base 3 of 729	$\log_{729} (729) + \log_{27} (729) + \log_{3} (729)$
40303	Simplify/Condense	log base 729 of 9+ log base 27 of 9+ log base 3 of 9	$\log_{729} (9) + \log_{27} (9) + \log_{3} (9)$
40304	Simplify	cos(-theta)-cos(theta)	$\cos (- θ) - \cos (θ)$
40305	Simplify/Condense	log base 8 of 0.5	$\log_{8} (0.5)$
40306	Simplify/Condense	log base 8 of 1/( square root of 8)	$\log_{8} (\frac{1}{\sqrt{8}})$
40307	Simplify/Condense	log base 8 of 16^( log of 1/10000)	$\log_{8} (16^{\log (\frac{1}{10000})})$
40308	Solve for x	square root of ax-b=c	$\sqrt{a x - b} = c$
40309	Simplify/Condense	log base 8 of 17x	$\log_{8} (17 x)$
40310	Simplify/Condense	log base 8 of 8*(3x)	$\log_{8} (8) \cdot (3 x)$
40311	Simplify/Condense	log base 8 of 9+ log base 8 of x	$\log_{8} (9) + \log_{8} (x)$
40312	Simplify/Condense	log base 81 of 6561+ log base 9 of 6561+ log base 3 of 6561	$\log_{81} (6561) + \log_{9} (6561) + \log_{3} (6561)$
40313	Solve for x	x-5 = square root of 2x-7	$x - 5 = \sqrt{2 x - 7}$
40314	Simplify/Condense	log base 9 of 14	$\log_{9} (14)$
40315	Simplify/Condense	log base 9 of 20- log base 9 of 4	$\log_{9} (20) - \log_{9} (4)$
40316	Solve for x	square root of x-2=3	$\sqrt{x - 2} = 3$
40317	Solve for x	natural log of x-35+ natural log of x+180=3 natural log of 6	$\ln (x - 35) + \ln (x + 180) = 3 \ln (6)$
40318	Simplify/Condense	log base a of x^3y^2z	$\log_{a} (x^{3} y^{2} z)$
40319	Simplify/Condense	log base a of (3(y^5))/(xz^3)	$\log_{a} (\frac{3 (y^{5})}{x z^{3}})$
40320	Simplify/Condense	log base b of (wy^3)/(w^4z)	$\log_{b} (\frac{w y^{3}}{w^{4} z})$
40321	Simplify/Condense	log base b of (x^2y)/(z^4)	$\log_{b} (\frac{x^{2} y}{z^{4}})$
40322	Simplify	(2 square root of 7-3)/( square root of 7-2)	$\frac{2 \sqrt{7} - 3}{\sqrt{7} - 2}$
40323	Simplify/Condense	log base 5 of 3+ log base 5 of 2- log base 5 of 3750	$\log_{5} (3) + \log_{5} (2) - \log_{5} (3750)$
40324	Simplify/Condense	log base 5 of 6.25* log base 5 of 100* log base 5 of 25	$\log_{5} (6.25) \cdot \log_{5} (100) \cdot \log_{5} (25)$
40325	Convert to Interval Notation	x^4>81	$x^{4} > 81$
40326	Simplify/Condense	log base 5 of 8	$\log_{5} (8)$
40327	Simplify/Condense	log base 5 of 89	$\log_{5} (89)$
40328	Simplify/Condense	log base 5 of x(x-1)	$\log_{5} (x (x - 1))$
40329	Simplify/Condense	log base 5 of x-2 log base 5 of y+3 log base 5 of z	$\log_{5} (x) - 2 \log_{5} (y) + 3 \log_{5} (z)$
40330	Simplify/Condense	log base 6 of (x^7)/(x-2)	$\log_{6} (\frac{x^{7}}{x - 2})$
40331	Find the Asymptotes	f(x)=(x-5)/(x^2-25)	$f (x) = \frac{x - 5}{x^{2} - 25}$
40332	Simplify/Condense	log base 6 of 1/(72d^4)	$\log_{6} (\frac{1}{72 d^{4}})$
40333	Simplify/Condense	log base 6 of 6^17	$\log_{6} (6^{17})$
40334	Simplify/Condense	log base 6 of 6^4	$\log_{6} (6^{4})$
40335	Simplify/Condense	log base 6 of square root of x- log base 6 of x^9	$\log_{6} (\sqrt{x}) - \log_{6} (x^{9})$
40336	Simplify/Condense	log base 6 of cube root of 1/6	$\log_{6} (\sqrt[3]{\frac{1}{6}})$
40337	Find the Other Trig Values in Quadrant I	tan(theta)=15/8	$\tan (θ) = \frac{15}{8}$
40338	Simplify/Condense	log base 5 of 1/15	$\log_{5} (\frac{1}{15})$
40339	Simplify/Condense	log base 5 of 125/y	$\log_{5} (\frac{125}{y})$
40340	Simplify/Condense	log base 5 of c^6	$\log_{5} (c^{6})$
40341	Simplify/Condense	log base 5 of 1- log base 5 of 250	$\log_{5} (1) - \log_{5} (250)$
40342	Simplify/Condense	log base 4 of x-4+2 log base 4 of x+4- log base 4 of x^3+2x^2-16x-32	$\log_{4} (x - 4) + 2 \log_{4} (x + 4) - \log_{4} (x^{3} + 2 x^{2} - 16 x - 32)$
40343	Convert to Polar Coordinates	(5,(3pi)/4)	$(5, \frac{3 π}{4})$
40344	Simplify/Condense	log base 4 of 19	$\log_{4} (19)$
40345	Simplify/Condense	log base 6 of 1296	$\log_{6} (1296)$
40346	Expand the Logarithmic Expression	log base B of 9	$\log_{B} (9)$
40347	Simplify/Condense	log base 6 of 32	$\log_{6} (32)$
40348	Simplify/Condense	log base 6 of 41	$\log_{6} (41)$
40349	Simplify/Condense	log base 6 of 7* log base 7 of 1296	$\log_{6} (7) \cdot \log_{7} (1296)$
40350	Simplify/Condense	log base 6 of 80	$\log_{6} (80)$
40351	Simplify/Condense	log base 6 of x+12+ log base 6 of x-12	$\log_{6} (x + 12) + \log_{6} (x - 12)$
40352	Simplify/Condense	log base 6 of x+2+1/6* log base 6 of x	$\log_{6} (x + 2) + \frac{1}{6} \cdot \log_{6} (x)$
40353	Simplify/Condense	log base 63 of x	$\log_{63} (x)$
40354	Simplify/Condense	log base 7 of ( sixth root of p fifth root of q)/(t^2)	$\log_{7} (\frac{\sqrt[6]{p} \sqrt[5]{q}}{t^{2}})$
40355	Expand the Logarithmic Expression	natural log of (e^3)/(x^4)	$\ln (\frac{e^{3}}{x^{4}})$
40356	Simplify/Condense	log base 7 of 4^3+ log base 7 of 16	$\log_{7} (4^{3}) + \log_{7} (16)$
40357	Simplify/Condense	log base 7 of x^2-11x+30- log base 7 of x^2-36+ log base 7 of x+6	$\log_{7} (x^{2} - 11 x + 30) - \log_{7} (x^{2} - 36) + \log_{7} (x + 6)$
40358	Simplify/Condense	log base 7 of 4* log base 4 of 49	$\log_{7} (4) \cdot \log_{4} (49)$
40359	Simplify/Condense	log base 7 of 4- log base 7 of 1+1	$\log_{7} (4) - \log_{7} (1 + 1)$
40360	Simplify/Condense	natural log of 10+4 natural log of x+4 natural log of x^2+10	$\ln (10) + 4 \ln (x) + 4 \ln (x^{2} + 10)$
40361	Simplify/Condense	natural log of 10- natural log of 2	$\ln (10) - \ln (2)$
40362	Simplify/Condense	natural log of 10- natural log of 5	$\ln (10) - \ln (5)$
40363	Solve for x	sin(x)-cos(2x)=0	$\sin (x) - \cos (2 x) = 0$
40364	Evaluate the Limit	limit as x approaches -6 of (2x^2+9x-18)/(x+6)	$lim_{x \to - 6} \frac{2 x^{2} + 9 x - 18}{x + 6}$
40365	Simplify	(sin(theta)+cos(theta))^2+(sin(theta)-cos(theta))^2	${(\sin (θ) + \cos (θ))}^{2} + {(\sin (θ) - \cos (θ))}^{2}$
40366	Find dx/dy	y=((1+2x)^(1/3))/((1-x)^3)	$y = \frac{{(1 + 2 x)}^{\frac{1}{3}}}{{(1 - x)}^{3}}$
40367	Find dx/dy	y=2 square root of x-9 cube root of x^2-4 fourth root of x^3+10 fifth root of x^4	$y = 2 \sqrt{x} - 9 \sqrt[3]{x^{2}} - 4 \sqrt[4]{x^{3}} + 10 \sqrt[5]{x^{4}}$
40368	Divide	1/(1/2)	$\frac{1}{\frac{1}{2}}$
40369	Simplify	(sin(theta))/(cos(theta))+(cos(theta))/(sin(theta))	$\frac{\sin (θ)}{\cos (θ)} + \frac{\cos (θ)}{\sin (θ)}$
40370	Simplify	1/(sec(theta)+tan(theta))+1/(sec(theta)-tan(theta))	$\frac{1}{\sec (θ) + \tan (θ)} + \frac{1}{\sec (θ) - \tan (θ)}$
40371	Find the Derivative - d/d@VAR	f(x)=3 square root of x-5 fourth root of x^3+13 fifth root of x^2-3/( cube root of x^2)	$f (x) = 3 \sqrt{x} - 5 \sqrt[4]{x^{3}} + 13 \sqrt[5]{x^{2}} - \frac{3}{\sqrt[3]{x^{2}}}$
40372	Simplify	sin(theta)(csc(theta)-sin(theta))	$\sin (θ (\csc (θ) - \sin (θ)))$
40373	Simplify	cot(x)(sec(x)-tan(x))	$\cot (x (\sec (x) - \tan (x)))$
40374	Evaluate	cos(105 degrees )^2-sin(105 degrees )^2	$\cos^{2} (105 °) - \sin^{2} (105 °)$
40375	Simplify	sec(x)^4-tan(x)^4	$\sec^{4} (x) - \tan^{4} (x)$
40376	Find dx/dy	y=(3x+2)/(4x-7)	$y = \frac{3 x + 2}{4 x - 7}$
40377	Simplify	(1-cos(theta))(csc(theta)+cot(theta))	$(1 - \cos (θ)) (\csc (θ) + \cot (θ))$
40378	Simplify	(cos(theta)^2-sin(theta)^2)/(sin(theta)^4-cos(theta)^4)	$\frac{\cos^{2} (θ) - \sin^{2} (θ)}{\sin^{4} (θ) - \cos^{4} (θ)}$
40379	Simplify	(cot(theta)+csc(theta))(cot(theta)-csc(theta))	$(\cot (θ) + \csc (θ)) (\cot (θ) - \csc (θ))$
40380	Graph	y=cos(x-pi/4)	$y = \cos (x - \frac{π}{4})$
40381	Find dx/dy	x^2y-xy^2+x^2+y^2=0	$x^{2} y - x y^{2} + x^{2} + y^{2} = 0$
40382	Simplify	cos(x)(sec(x)-cos(x))	$\cos (x (\sec (x) - \cos (x)))$
40383	Graph	y=arccos(x)	$y = \arccos (x)$
40384	Simplify	sin(theta)^4-cos(theta)^4	$\sin^{4} (θ) - \cos^{4} (θ)$
40385	Divide	(2pi)/(pi/4)	$\frac{2 π}{\frac{π}{4}}$
40386	Graph	r=2+2cos(theta)	$r = 2 + 2 \cos (θ)$
40387	Graph	(4pi)/3	$\frac{4 π}{3}$
40388	Find the Vertex	f(x)=3(x-7)^2-4	$f (x) = 3 {(x - 7)}^{2} - 4$
40389	Find the Second Derivative	x^2-xy+y^2=3	$x^{2} - x y + y^{2} = 3$
40390	Find All Complex Solutions	sin(x)=( square root of 3)/2	$\sin (x) = \frac{\sqrt{3}}{2}$
40391	Find the Other Trig Values in Quadrant II	sin(theta)=8/17	$\sin (θ) = \frac{8}{17}$
40392	Divide	(2pi)/(pi/3)	$\frac{2 π}{\frac{π}{3}}$
40393	Find All Complex Solutions	cos(2theta)=( square root of 3)/2	$\cos (2 θ) = \frac{\sqrt{3}}{2}$
40394	Find the Asymptotes	y=6tan(0.2x)	$y = 6 \tan (0.2 x)$
40395	Verify the Identity	sin(theta)(cot(theta)+tan(theta))=sec(theta)	$\sin (θ (\cot (θ) + \tan (θ))) = \sec (θ)$
40396	Divide	4/2	$\frac{4}{2}$
40397	Find the Trig Value	tan(theta) = square root of 3	$\tan (θ) = \sqrt{3}$
40398	Find the Other Trig Values in Quadrant IV	sin(theta)=-7/25	$\sin (θ) = - \frac{7}{25}$
40399	Find the Value Using the Unit Circle	(5pi)/6	$\frac{5 π}{6}$
40400	Find the Degree	cot(theta)=( square root of 3)/3	$\cot (θ) = \frac{\sqrt{3}}{3}$