Solve for x log base 3 of 2x-9=3

$\log_{3} (2 x - 9) = 3$

Rewrite $\log_{3} (2 x - 9) = 3$ 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 $b^{y} = x$ .

$3^{3} = 2 x - 9$

Solve for $x$ .

Rewrite the equation as $2 x - 9 = 3^{3}$ .

$2 x - 9 = 3^{3}$

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

$2 x - 9 = 27$

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

Add $9$ to both sides of the equation.

$2 x = 27 + 9$

Add $27$ and $9$ .

$2 x = 36$

Divide each term in $2 x = 36$ by $2$ and simplify.

Divide each term in $2 x = 36$ by $2$ .

$\frac{2 x}{2} = \frac{36}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{36}{2}$

Divide $x$ by $1$ .

$x = \frac{36}{2}$

Simplify the right side.

Divide $36$ by $2$ .

$x = 18$

Solve for x log base 3 of 2x-9=3

Related Questions

Support LCMGCF.com by disabling your adblocker.