Solve Ans n that 3 ^ (2x + 1) = 243 , find the value of x. | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$3 ^ { 2 x + 1 } = 243 , x$$

Solve for x

$x=2$

Steps Using Definition of Logarithm

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

$$3^{2x+1}=243$$

Take the logarithm of both sides of the equation.

$$\log(3^{2x+1})=\log(243)$$

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

$$\left(2x+1\right)\log(3)=\log(243)$$

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

$$2x+1=\frac{\log(243)}{\log(3)}$$

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

$$2x+1=\log_{3}\left(243\right)$$

Subtract $1$ from both sides of the equation.

$$2x=5-1$$

Divide both sides by $2$.

$$x=\frac{4}{2}$$

Solve for x (complex solution)

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