How to solve 8 ^ x = 16

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 8 ^ x = 16 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

$$8^{x}=16$$

$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$

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

$$8^{x}=16$$

Take the logarithm of both sides of the equation.

$$\log(8^{x})=\log(16)$$

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

$$x\log(8)=\log(16)$$

Divide both sides by $\log(8)$.

$$x=\frac{\log(16)}{\log(8)}$$

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

$$x=\log_{8}\left(16\right)$$

$x=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{4}{3}$
$n_{1}\in \mathrm{Z}$