Solve for x log base 3 of 2x+3=4

$\log_{3} (2 x + 3) = 4$

Rewrite $\log_{3} (2 x + 3) = 4$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$3^{4} = 2 x + 3$

Solve for $x$ .

Rewrite the equation as $2 x + 3 = 3^{4}$ .

$2 x + 3 = 3^{4}$

Raise $3$ to the power of $4$ .

$2 x + 3 = 81$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$2 x = 81 - 3$

Subtract $3$ from $81$ .

$2 x = 78$

Divide each term in $2 x = 78$ by $2$ and simplify.

Divide each term in $2 x = 78$ by $2$ .

$\frac{2 x}{2} = \frac{78}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{78}{2}$

Divide $x$ by $1$ .

$x = \frac{78}{2}$

Simplify the right side.

Divide $78$ by $2$ .

$x = 39$

Solve for x log base 3 of 2x+3=4

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