Solve for n log base 9 of 15-4n=1/2

$\log_{9} (15 - 4 n) = \frac{1}{2}$

Step 1

Rewrite $\log_{9} (15 - 4 n) = \frac{1}{2}$ 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 $b^{y} = x$ .

$9^{\frac{1}{2}} = 15 - 4 n$

Step 2

Solve for $n$ .

Rewrite the equation as $15 - 4 n = 9^{\frac{1}{2}}$ .

$15 - 4 n = 9^{\frac{1}{2}}$

Simplify $9^{\frac{1}{2}}$ .

Rewrite.

$15 - 4 n = 0 + 0 + 9^{\frac{1}{2}}$

Simplify the expression.

Rewrite $9$ as $3^{2}$ .

$15 - 4 n = {(3^{2})}^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$15 - 4 n = 3^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$15 - 4 n = 3^{2 (\frac{1}{2})}$

Rewrite the expression.

$15 - 4 n = 3^{1}$

Evaluate the exponent.

$15 - 4 n = 3$

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

Subtract $15$ from both sides of the equation.

$- 4 n = 3 - 15$

Subtract $15$ from $3$ .

$- 4 n = - 12$

Divide each term in $- 4 n = - 12$ by $- 4$ and simplify.

Divide each term in $- 4 n = - 12$ by $- 4$ .

$\frac{- 4 n}{- 4} = \frac{- 12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 n}{- 4} = \frac{- 12}{- 4}$

Divide $n$ by $1$ .

$n = \frac{- 12}{- 4}$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$n = 3$

Solve for n log base 9 of 15-4n=1/2

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