Solve 87^2=5^x

$${ 87 }^{ 2 } = { 5 }^{ x }$$

Solve for x

$$x=2\log_{5}\left(87\right)\approx 5.549649457$$

Steps Using Definition of Logarithm

Calculate 87 to the power of 2 and get 7569.

$$7569=5^{x}$$

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

$$5^{x}=7569$$

Take the logarithm of both sides of the equation.

$$\log(5^{x})=\log(7569)$$

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

$$x\log(5)=\log(7569)$$

Divide both sides by \log(5).

$$x=\frac{\log(7569)}{\log(5)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{5}\left(7569\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+2\log_{5}\left(87\right)$$

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