Solve 14925.7=1.026^x

$$14925.7 = { 1.026 }^{ x }$$

Solve for x

$$x=\log_{1.026}\left(14925.7\right)\approx 374.432548851$$

Steps Using Definition of Logarithm

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

$$1.026^{x}=14925.7$$

Take the logarithm of both sides of the equation.

$$\log(1.026^{x})=\log(14925.7)$$

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

$$x\log(1.026)=\log(14925.7)$$

Divide both sides by \log(1.026).

$$x=\frac{\log(14925.7)}{\log(1.026)}$$

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

$$x=\log_{1.026}\left(14925.7\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.026)}+\log_{1.026}\left(14925.7\right)$$

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