# How do you solve log 8 - (1/3) log x = log 2?

Mar 9, 2016

$x = 64$

#### Explanation:

From the laws of logs we may write this as

$\log \left(\frac{8}{x} ^ \left(\frac{1}{3}\right)\right) = \log 2$

Now taking the antilog on both sides and cross-multiplying yields

$2 {x}^{\frac{1}{3}} = 8$

Now applying laws of exponents and surds and simplifying, we get

$\sqrt[3]{x} = 4$

$\therefore x = {4}^{3} = 64$