Solve 1.2^x=10

$${ 1.2 }^{ x } =10$$

Solve for x

$$x=\log_{1.2}\left(10\right)\approx 12.629253137$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$1.2^{x}=10$$

Take the logarithm of both sides of the equation.

$$\log(1.2^{x})=\log(10)$$

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

$$x\log(1.2)=\log(10)$$

Divide both sides by \log(1.2).

$$x=\frac{\log(10)}{\log(1.2)}$$

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

$$x=\log_{1.2}\left(10\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.2)}+\log_{1.2}\left(10\right)$$

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