Solve for n log base 3 of 4n-17=5

$\log_{3} (4 n - 17) = 5$

Step 1

Rewrite $\log_{3} (4 n - 17) = 5$ 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 $b^{y} = x$ .

$3^{5} = 4 n - 17$

Step 2

Solve for $n$ .

Rewrite the equation as $4 n - 17 = 3^{5}$ .

$4 n - 17 = 3^{5}$

Raise $3$ to the power of $5$ .

$4 n - 17 = 243$

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

Add $17$ to both sides of the equation.

$4 n = 243 + 17$

Add $243$ and $17$ .

$4 n = 260$

Divide each term in $4 n = 260$ by $4$ and simplify.

Divide each term in $4 n = 260$ by $4$ .

$\frac{4 n}{4} = \frac{260}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 n}{4} = \frac{260}{4}$

Divide $n$ by $1$ .

$n = \frac{260}{4}$

Simplify the right side.

Divide $260$ by $4$ .

$n = 65$

Solve for n log base 3 of 4n-17=5

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