Basic Math Examples

$\frac{\log (a)}{\log (6)} = y$

Step 1

Multiply both sides of the equation by $\log (6)$ .

$\log (6) \frac{\log (a)}{\log (6)} = \log (6) y$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $\log (6)$ .

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Step 2.1.1.1

Cancel the common factor.

$\log (6) \frac{\log (a)}{\log (6)} = \log (6) y$

Step 2.1.1.2

Rewrite the expression.

$\log (a) = \log (6) y$

Step 2.2

Simplify the right side.

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Step 2.2.1

Reorder factors in $\log (6) y$ .

$\log (a) = y \log (6)$

Step 3

Rewrite $\log (a) = y \log (6)$ 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 $b^{y} = x$ .

$10^{y \log (6)} = a$

Step 4

Rewrite the equation as $a = 10^{y \log (6)}$ .

$a = 10^{y \log (6)}$