Logs in equations

Question

I am working on an excel project and had a few questions. I need to solve $\log(x)/\log(2)=-0.145509439$. I already know the answer, which is $0.90406$, but I do not know how to solve the equation.

Answer 1

You need to use the change of base formula, which gives you $\log_2(x) = -0.145509439$ and then you know that $2^{-0.145509439} = x$ and arithmetic gives you $x=.90406$

Answer 2

Multiply both sides by $\log(2)$, and then exponentiate to turn the $\log(x)$ into just $x$.

Answer 3

So we have $\frac{logx}{log2}=-0.145509439$ multiply both sides by $log2$ to have $logx=-0.100859...$ and then apply exponential function to both sides. $e^{logx}=e^{-0.100859...}$ and you should know that $e^{logx}=x$ hence $x=e^{-0.100859...}=0.9046...$