Solve for x 4+5 log base 3 of x+6=8

$4 + 5 \log_{3} (x + 6) = 8$

Step 1

Move all terms not containing $\log_{3} (x + 6)$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$5 \log_{3} (x + 6) = 8 - 4$

Subtract $4$ from $8$ .

$5 \log_{3} (x + 6) = 4$

Step 2

Divide each term in $5 \log_{3} (x + 6) = 4$ by $5$ and simplify.

Divide each term in $5 \log_{3} (x + 6) = 4$ by $5$ .

$\frac{5 \log_{3} (x + 6)}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 \log_{3} (x + 6)}{5} = \frac{4}{5}$

Divide $\log_{3} (x + 6)$ by $1$ .

$\log_{3} (x + 6) = \frac{4}{5}$

Step 3

Rewrite $\log_{3} (x + 6) = \frac{4}{5}$ 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 $b^{y} = x$ .

$3^{\frac{4}{5}} = x + 6$

Step 4

Solve for $x$ .

Rewrite the equation as $x + 6 = 3^{\frac{4}{5}}$ .

$x + 6 = 3^{\frac{4}{5}}$

Subtract $6$ from both sides of the equation.

$x = 3^{\frac{4}{5}} - 6$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 3^{\frac{4}{5}} - 6$

Decimal Form:

$x = - 3.59177531 \dots$

Solve for x 4+5 log base 3 of x+6=8

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