Solve e^3m+6=33

$$e ^ { 3 m + 6 } = 33$$

Solve for m

$$m=\frac{\ln(33)-6}{3}\approx -0.83449748$$

Steps Using Definition of Logarithm

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

$$e^{3m+6}=33$$

Take the logarithm of both sides of the equation.

$$\log(e^{3m+6})=\log(33)$$

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

$$\left(3m+6\right)\log(e)=\log(33)$$

Divide both sides by \log(e).

$$3m+6=\frac{\log(33)}{\log(e)}$$

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

$$3m+6=\log_{e}\left(33\right)$$

Subtract 6 from both sides of the equation.

$$3m=\ln(33)-6$$

Divide both sides by 3.

$$m=\frac{\ln(33)-6}{3}$$