Solve 4120^-m-5=86

$$4120 ^ { - m } - 5 = 86$$

Solve for m

$$m=-\log_{4120}\left(91\right)\approx -0.541935573$$

Steps Using Definition of Logarithm

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

$$4120^{-m}-5=86$$

Add 5 to both sides of the equation.

$$4120^{-m}=91$$

Take the logarithm of both sides of the equation.

$$\log(4120^{-m})=\log(91)$$

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

$$-m\log(4120)=\log(91)$$

Divide both sides by \log(4120).

$$-m=\frac{\log(91)}{\log(4120)}$$

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

$$-m=\log_{4120}\left(91\right)$$

Divide both sides by -1.

$$m=\frac{\log_{4120}\left(91\right)}{-1}$$