How to solve (3)^(2x-1)=81

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)^(2x-1)=81 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$${ 3 }^{ 2x-1 } =81$$

Solve for x

$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$

Steps Using Definition of Logarithm

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

$$3^{2x-1}=81$$

Take the logarithm of both sides of the equation.

$$\log(3^{2x-1})=\log(81)$$

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

$$\left(2x-1\right)\log(3)=\log(81)$$

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

$$2x-1=\frac{\log(81)}{\log(3)}$$

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

$$2x-1=\log_{3}\left(81\right)$$

Add $1$ to both sides of the equation.

$$2x=4-\left(-1\right)$$

Divide both sides by $2$.

$$x=\frac{5}{2}$$

Show Solution

Solve for x (complex solution)

$x=\frac{i\pi n_{1}}{\ln(3)}+\frac{5}{2}$
$n_{1}\in \mathrm{Z}$