Algebra Examples

$10 \log (x) + \frac{2}{3} \log (64)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $10 \log (x)$ by moving $10$ inside the logarithm.

$\log (x^{10}) + \frac{2}{3} \cdot \log (64)$

Step 1.2

Simplify $\frac{2}{3} \log (64)$ by moving $\frac{2}{3}$ inside the logarithm.

$\log (x^{10}) + \log (64^{\frac{2}{3}})$

Step 1.3

Rewrite $64$ as $4^{3}$ .

$\log (x^{10}) + \log ({(4^{3})}^{\frac{2}{3}})$

Step 1.4

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

$\log (x^{10}) + \log (4^{3 (\frac{2}{3})})$

Step 1.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.5.1

Cancel the common factor.

$\log (x^{10}) + \log (4^{3 (\frac{2}{3})})$

Step 1.5.2

Rewrite the expression.

$\log (x^{10}) + \log (4^{2})$

Step 1.6

Raise $4$ to the power of $2$ .

$\log (x^{10}) + \log (16)$

Step 2

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

$\log (x^{10} \cdot 16)$

Step 3

Move $16$ to the left of $x^{10}$ .

$\log (16 x^{10})$