Answer
$x=\dfrac{\log\dfrac{5}{4}}{5}\approx0.019382$
Work Step by Step
$4(1+10^{5x})=9$
First, let's solve for $10^{5x}$:
$1+10^{5x}=\dfrac{9}{4}$
$10^{5x}=\dfrac{9}{4}-1$
$10^{5x}=\dfrac{5}{4}$
Apply $\log$ to both sides of the equation:
$\log10^{5x}=\log\dfrac{5}{4}$
The exponent $5x$ can be taken down to multiply in front of its respective $\log$:
$5x\log10=\log\dfrac{5}{4}$
Since $\log10=1$, the equation becomes:
$5x=\log\dfrac{5}{4}$
Solve for $x$:
$x=\dfrac{\log\dfrac{5}{4}}{5}\approx0.019382$
