# Finding values of x for logarithm The question is to find the numbers of x which satisfy the equation. log_x 10=log_4 100.

Finding values of x for logarithm
The question is to find the numbers of x which satisfy the equation.
${\mathrm{log}}_{x}10={\mathrm{log}}_{4}100.$
I have
$\begin{array}{rl}\frac{\mathrm{ln}10}{\mathrm{ln}x}& =\frac{\mathrm{ln}100}{\mathrm{ln}4}\\ \frac{\mathrm{ln}10}{\mathrm{ln}x}& =\frac{2\mathrm{ln}10}{2\mathrm{ln}2}\end{array}$
What would I do after this step?
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Kaleb Harrell
All right. First multiply by $ln\left(x\right)$ and by $ln\left(2\right)$. You get
$ln\left(10\right)ln\left(2\right)=ln\left(10\right)ln\left(x\right)$
Now divide by $ln\left(10\right)$. This gives you
$ln\left(2\right)=ln\left(x\right)$
Now you apply the exponential function on both sides to get rid of the logarithm:
$\underset{=x}{\underset{⏟}{{e}^{ln\left(x\right)}}}=\underset{=2}{\underset{⏟}{{e}^{ln\left(2\right)}}}$
So $x=2$