Solve for x 3 log of 1-2x=6

$3 \log (1 - 2 x) = 6$

Divide each term in $3 \log (1 - 2 x) = 6$ by $3$ and simplify.

Divide each term in $3 \log (1 - 2 x) = 6$ by $3$ .

$\frac{3 \log (1 - 2 x)}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \log (1 - 2 x)}{3} = \frac{6}{3}$

Divide $\log (1 - 2 x)$ by $1$ .

$\log (1 - 2 x) = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$\log (1 - 2 x) = 2$

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

$10^{2} = 1 - 2 x$

Solve for $x$ .

Rewrite the equation as $1 - 2 x = 10^{2}$ .

$1 - 2 x = 10^{2}$

Raise $10$ to the power of $2$ .

$1 - 2 x = 100$

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

Subtract $1$ from both sides of the equation.

$- 2 x = 100 - 1$

Subtract $1$ from $100$ .

$- 2 x = 99$

Divide each term in $- 2 x = 99$ by $- 2$ and simplify.

Divide each term in $- 2 x = 99$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{99}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{99}{- 2}$

Divide $x$ by $1$ .

$x = \frac{99}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{99}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{99}{2}$

Decimal Form:

$x = - 49.5$

Mixed Number Form:

$x = - 49 \frac{1}{2}$

Solve for x 3 log of 1-2x=6

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