Solve 15*(107)^x=4

$$15 \times ( 107 ) ^ { x } = 4$$

Solve for x

$$x=\log_{107}\left(\frac{4}{15}\right)\approx -0.282859888$$

Steps Using Definition of Logarithm

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

$$15\times 107^{x}=4$$

Divide both sides by 15.

$$107^{x}=\frac{4}{15}$$

Take the logarithm of both sides of the equation.

$$\log(107^{x})=\log(\frac{4}{15})$$

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

$$x\log(107)=\log(\frac{4}{15})$$

Divide both sides by \log(107).

$$x=\frac{\log(\frac{4}{15})}{\log(107)}$$

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

$$x=\log_{107}\left(\frac{4}{15}\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(107)}+\log_{107}\left(\frac{4}{15}\right)$$

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