Precalculus Examples

$\log_{7} (\frac{y}{3}) = x$

Step 1

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

$7^{x} = \frac{y}{3}$

Step 2

Solve for $y$ .

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Step 2.1

Rewrite the equation as $\frac{y}{3} = 7^{x}$ .

$\frac{y}{3} = 7^{x}$

Step 2.2

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 \cdot 7^{x}$

Step 2.3

Simplify the left side.

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Step 2.3.1

Cancel the common factor of $3$ .

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Step 2.3.1.1

Cancel the common factor.

$3 \frac{y}{3} = 3 \cdot 7^{x}$

Step 2.3.1.2

Rewrite the expression.

$y = 3 \cdot 7^{x}$