Solve for v -6+ log of 6v=-7

$- 6 + \log (6 v) = - 7$

Move all terms not containing $\log (6 v)$ to the right side of the equation.

Add $6$ to both sides of the equation.

$\log (6 v) = - 7 + 6$

Add $- 7$ and $6$ .

$\log (6 v) = - 1$

Rewrite $\log (6 v) = - 1$ 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 $b^{y} = x$ .

$10^{- 1} = 6 v$

Solve for $v$ .

Rewrite the equation as $6 v = 10^{- 1}$ .

$6 v = 10^{- 1}$

Divide each term in $6 v = 10^{- 1}$ by $6$ and simplify.

Divide each term in $6 v = 10^{- 1}$ by $6$ .

$\frac{6 v}{6} = \frac{10^{- 1}}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 v}{6} = \frac{10^{- 1}}{6}$

Divide $v$ by $1$ .

$v = \frac{10^{- 1}}{6}$

Simplify the right side.

Move $10^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$v = \frac{1}{6 \cdot 10}$

Multiply $6$ by $10$ .

$v = \frac{1}{60}$

The result can be shown in multiple forms.

Exact Form:

$v = \frac{1}{60}$

Decimal Form:

$v = 0.01\overline{6}$

Solve for v -6+ log of 6v=-7

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