# Question #8252f

Nov 6, 2016

depends on which logs you use.

#### Explanation:

$\log \left({2}^{{x}^{3}}\right)$ is the same as ${x}^{3} \log \left(2\right)$

so we end up with:$\text{ } {x}^{3} \log \left(2\right) = 6$

$\implies {x}^{3} = \frac{6}{\log} \left(2\right)$

$x = \sqrt[3]{\frac{6}{\log} \left(2\right)}$

The value of $x$ will vary depending on what type of logs you use.

The usual is either ${\log}_{10} \text{ or } {\log}_{e}$ where ${\log}_{e}$ is normally written as ln

$x = \sqrt[3]{\frac{6}{\log} _ 10 \left(2\right)} \approx 2.7113$ to 4 decimal places

$x = \sqrt[3]{\frac{6}{\ln} \left(2\right)} \approx 2.0533$ to 4 decimal places