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Answer 1 · 2016-11-06T17:57:57

depends on which logs you use.

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

so we end up with: $x^{3} log (2) = 6$ $" "x^3log(2)=6$

$\Rightarrow x^{3} = \frac{6}{log (2)}$ $=>x^3=6/log(2)$

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

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

The usual is either ${log}_{10} or {log}_{e}$ $log_10" or "log_e$ where ${log}_{e}$ $log_e$ is normally written as ln

$x = \sqrt[3]{\frac{6}{{log}_{10} (2)}} \approx 2.7113$ $x= root(3)(6/log_10(2)) ~~2.7113$ to 4 decimal places

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