Solve 13^x-6.2=67

$$13 ^ { x } - 6.2 = 67$$

Solve for x

$$x=\log_{13}\left(73.2\right)\approx 1.673793445$$

Steps Using Definition of Logarithm

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

$$13^{x}-6.2=67$$

Add 6.2 to both sides of the equation.

$$13^{x}=73.2$$

Take the logarithm of both sides of the equation.

$$\log(13^{x})=\log(73.2)$$

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

$$x\log(13)=\log(73.2)$$

Divide both sides by \log(13).

$$x=\frac{\log(73.2)}{\log(13)}$$

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

$$x=\log_{13}\left(73.2\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(13)}+\log_{13}\left(73.2\right)$$

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