Solve 1/4=10^95x

$$\frac{ 1 }{ 4 } = { 10 }^{ 95x }$$

Solve for x

$$x=-\frac{2\log(2)}{95}\approx -0.006337474$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$10^{95x}=\frac{1}{4}$$

Take the logarithm of both sides of the equation.

$$\log(10^{95x})=\log(\frac{1}{4})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$95x\log(10)=\log(\frac{1}{4})$$

Divide both sides by 95.

$$x=-\frac{2\log(2)}{95}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{95\ln(10)}-\frac{2\log_{10}\left(2\right)}{95}$$

$$n_{1}\in \mathrm{Z}$$