How to solve (3)^(x)=500

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 (3)^(x)=500 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

$${ 3 }^{ x } =500$$

$x=\log_{3}\left(500\right)\approx 5.656780069$

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

$$3^{x}=500$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(500)$$

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

$$x\log(3)=\log(500)$$

Divide both sides by $\log(3)$.

$$x=\frac{\log(500)}{\log(3)}$$

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

$$x=\log_{3}\left(500\right)$$

$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(500\right)$
$n_{1}\in \mathrm{Z}$