Solve for x 7- log base 3 of 8x=2

$7 - \log_{3} (8 x) = 2$

Step 1

Move all terms not containing $\log_{3} (8 x)$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- \log_{3} (8 x) = 2 - 7$

Subtract $7$ from $2$ .

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

Step 2

Divide each term in $- \log_{3} (8 x) = - 5$ by $- 1$ and simplify.

Divide each term in $- \log_{3} (8 x) = - 5$ by $- 1$ .

$\frac{- \log_{3} (8 x)}{- 1} = \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\log_{3} (8 x)}{1} = \frac{- 5}{- 1}$

Divide $\log_{3} (8 x)$ by $1$ .

$\log_{3} (8 x) = \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

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

Step 3

Rewrite $\log_{3} (8 x) = 5$ 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 $b^{y} = x$ .

$3^{5} = 8 x$

Step 4

Solve for $x$ .

Rewrite the equation as $8 x = 3^{5}$ .

$8 x = 3^{5}$

Divide each term in $8 x = 3^{5}$ by $8$ and simplify.

Divide each term in $8 x = 3^{5}$ by $8$ .

$\frac{8 x}{8} = \frac{3^{5}}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{3^{5}}{8}$

Divide $x$ by $1$ .

$x = \frac{3^{5}}{8}$

Simplify the right side.

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

$x = \frac{243}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{243}{8}$

Decimal Form:

$x = 30.375$

Mixed Number Form:

$x = 30 \frac{3}{8}$

Solve for x 7- log base 3 of 8x=2

Related Questions

Support LCMGCF.com by disabling your adblocker.