Solve for x 2 log base 7 of 1-2x=12

$2 \log_{7} (1 - 2 x) = 12$

Step 1

Divide each term in $2 \log_{7} (1 - 2 x) = 12$ by $2$ and simplify.

Divide each term in $2 \log_{7} (1 - 2 x) = 12$ by $2$ .

$\frac{2 \log_{7} (1 - 2 x)}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \log_{7} (1 - 2 x)}{2} = \frac{12}{2}$

Divide $\log_{7} (1 - 2 x)$ by $1$ .

$\log_{7} (1 - 2 x) = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$\log_{7} (1 - 2 x) = 6$

Step 2

Rewrite $\log_{7} (1 - 2 x) = 6$ 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 $b^{y} = x$ .

$7^{6} = 1 - 2 x$

Step 3

Solve for $x$ .

Rewrite the equation as $1 - 2 x = 7^{6}$ .

$1 - 2 x = 7^{6}$

Raise $7$ to the power of $6$ .

$1 - 2 x = 117649$

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

Subtract $1$ from both sides of the equation.

$- 2 x = 117649 - 1$

Subtract $1$ from $117649$ .

$- 2 x = 117648$

Divide each term in $- 2 x = 117648$ by $- 2$ and simplify.

Divide each term in $- 2 x = 117648$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{117648}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{117648}{- 2}$

Divide $x$ by $1$ .

$x = \frac{117648}{- 2}$

Simplify the right side.

Divide $117648$ by $- 2$ .

$x = - 58824$

Solve for x 2 log base 7 of 1-2x=12

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