Algebra Examples

$\log (x^{4}) + \frac{1}{2} \log (x^{4})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $\frac{1}{2} \log (x^{4})$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (x^{4}) + \log ({(x^{4})}^{\frac{1}{2}})$

Step 1.2

Multiply the exponents in ${(x^{4})}^{\frac{1}{2}}$ .

Tap for more steps...

Step 1.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (x^{4}) + \log (x^{4 (\frac{1}{2})})$

Step 1.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.2.1

Factor $2$ out of $4$ .

$\log (x^{4}) + \log (x^{2 (2) \frac{1}{2}})$

Step 1.2.2.2

Cancel the common factor.

$\log (x^{4}) + \log (x^{2 \cdot 2 \frac{1}{2}})$

Step 1.2.2.3

Rewrite the expression.

$\log (x^{4}) + \log (x^{2})$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x^{4} x^{2})$

Step 3

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log (x^{4 + 2})$

Step 3.2

Add $4$ and $2$ .

$\log (x^{6})$