Solve 100*0.05^x=150

$$100 \times { 0.05 }^{ x } =150$$

Solve for x

$$x=-\log_{20}\left(1.5\right)\approx -0.135347578$$

Steps Using Definition of Logarithm

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

$$100\times 0.05^{x}=150$$

Divide both sides by 100.

$$0.05^{x}=\frac{3}{2}$$

Take the logarithm of both sides of the equation.

$$\log(0.05^{x})=\log(\frac{3}{2})$$

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

$$x\log(0.05)=\log(\frac{3}{2})$$

Divide both sides by \log(0.05).

$$x=\frac{\log(\frac{3}{2})}{\log(0.05)}$$

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

$$x=\log_{0.05}\left(\frac{3}{2}\right)$$

Solve for x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{\ln(20)}-\log_{20}\left(1.5\right)$$

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