Solve 6(0.24)^x+18=126

$$6 ( 0.24 ) ^ { x } + 18 = 126$$

Solve for x

$$x=\log_{0.24}\left(18\right)\approx -2.025323126$$

Steps Using Definition of Logarithm

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

$$6\times 0.24^{x}+18=126$$

Subtract 18 from both sides of the equation.

$$6\times 0.24^{x}=108$$

Divide both sides by 6.

$$0.24^{x}=18$$

Take the logarithm of both sides of the equation.

$$\log(0.24^{x})=\log(18)$$

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

$$x\log(0.24)=\log(18)$$

Divide both sides by \log(0.24).

$$x=\frac{\log(18)}{\log(0.24)}$$

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

$$x=\log_{0.24}\left(18\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.24)}+\log_{0.24}\left(18\right)$$

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