Solve 1066.667=1.097^x

$$1066.667 = 1.097 ^ { x }$$

Solve for x

$$x=\log_{1.097}\left(1066.667\right)\approx 75.311684714$$

Steps Using Definition of Logarithm

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

$$1.097^{x}=1066.667$$

Take the logarithm of both sides of the equation.

$$\log(1.097^{x})=\log(1066.667)$$

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

$$x\log(1.097)=\log(1066.667)$$

Divide both sides by \log(1.097).

$$x=\frac{\log(1066.667)}{\log(1.097)}$$

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

$$x=\log_{1.097}\left(1066.667\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.097)}+\log_{1.097}\left(1066.667\right)$$

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