Solve for x log base 5 of 8-7x=3

$\log_{5} (8 - 7 x) = 3$

Step 1

Rewrite $\log_{5} (8 - 7 x) = 3$ 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 $b^{y} = x$ .

$5^{3} = 8 - 7 x$

Step 2

Solve for $x$ .

Rewrite the equation as $8 - 7 x = 5^{3}$ .

$8 - 7 x = 5^{3}$

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

$8 - 7 x = 125$

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

Subtract $8$ from both sides of the equation.

$- 7 x = 125 - 8$

Subtract $8$ from $125$ .

$- 7 x = 117$

Divide each term in $- 7 x = 117$ by $- 7$ and simplify.

Divide each term in $- 7 x = 117$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{117}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{117}{- 7}$

Divide $x$ by $1$ .

$x = \frac{117}{- 7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{117}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{117}{7}$

Decimal Form:

$x = - 16.71428571 \dots$

Mixed Number Form:

$x = - 16 \frac{5}{7}$

Solve for x log base 5 of 8-7x=3

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