Solve 11e^24x=7.5

$$11 { e }^{ 24x } =7.5$$

Solve for x

$$x=\frac{\ln(\frac{15}{22})}{24}\approx -0.015958011$$

Steps Using Definition of Logarithm

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

$$11e^{24x}=7.5$$

Divide both sides by 11.

$$e^{24x}=\frac{15}{22}$$

Take the logarithm of both sides of the equation.

$$\log(e^{24x})=\log(\frac{15}{22})$$

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

$$24x\log(e)=\log(\frac{15}{22})$$

Divide both sides by \log(e).

$$24x=\frac{\log(\frac{15}{22})}{\log(e)}$$

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

$$24x=\log_{e}\left(\frac{15}{22}\right)$$

Divide both sides by 24.

$$x=\frac{\ln(\frac{15}{22})}{24}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{12}+\frac{\ln(\frac{15}{22})}{24}$$

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