Solve for w 9 log base 6 of 5w+6+3=30

$9 \log_{6} (5 w + 6) + 3 = 30$

Move all terms not containing $\log_{6} (5 w + 6)$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$9 \log_{6} (5 w + 6) = 30 - 3$

Subtract $3$ from $30$ .

$9 \log_{6} (5 w + 6) = 27$

Divide each term in $9 \log_{6} (5 w + 6) = 27$ by $9$ and simplify.

Divide each term in $9 \log_{6} (5 w + 6) = 27$ by $9$ .

$\frac{9 \log_{6} (5 w + 6)}{9} = \frac{27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 \log_{6} (5 w + 6)}{9} = \frac{27}{9}$

Divide $\log_{6} (5 w + 6)$ by $1$ .

$\log_{6} (5 w + 6) = \frac{27}{9}$

Simplify the right side.

Divide $27$ by $9$ .

$\log_{6} (5 w + 6) = 3$

Rewrite $\log_{6} (5 w + 6) = 3$ 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 $b^{y} = x$ .

$6^{3} = 5 w + 6$

Solve for $w$ .

Rewrite the equation as $5 w + 6 = 6^{3}$ .

$5 w + 6 = 6^{3}$

Raise $6$ to the power of $3$ .

$5 w + 6 = 216$

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

Subtract $6$ from both sides of the equation.

$5 w = 216 - 6$

Subtract $6$ from $216$ .

$5 w = 210$

Divide each term in $5 w = 210$ by $5$ and simplify.

Divide each term in $5 w = 210$ by $5$ .

$\frac{5 w}{5} = \frac{210}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 w}{5} = \frac{210}{5}$

Divide $w$ by $1$ .

$w = \frac{210}{5}$

Simplify the right side.

Divide $210$ by $5$ .

$w = 42$

Solve for w 9 log base 6 of 5w+6+3=30

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