Solve 5(11.9)^(x)=298

$$5 ( 11.9 ) ^ { ( x ) } = 298$$

Solve for x

$$x=\log_{11.9}\left(59.6\right)\approx 1.650552066$$

Steps Using Definition of Logarithm

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

$$5\times 11.9^{x}=298$$

Divide both sides by 5.

$$11.9^{x}=\frac{298}{5}$$

Take the logarithm of both sides of the equation.

$$\log(11.9^{x})=\log(\frac{298}{5})$$

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

$$x\log(11.9)=\log(\frac{298}{5})$$

Divide both sides by \log(11.9).

$$x=\frac{\log(\frac{298}{5})}{\log(11.9)}$$

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

$$x=\log_{11.9}\left(\frac{298}{5}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(11.9)}+\log_{11.9}\left(59.6\right)$$

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