Precalculus Examples

$\log_{4} (x) - \log_{4} (5) = \log_{4} (60)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (\frac{x}{5}) = \log_{4} (60)$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$\frac{x}{5} = 60$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot 60$

Step 3.2

Simplify both sides of the equation.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot 60$

Step 3.2.1.1.2

Rewrite the expression.

$x = 5 \cdot 60$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Multiply $5$ by $60$ .

$x = 300$