Precalculus Examples

$\log (x) - \log (6) = 2 \log (4)$

Step 1

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

$\log (\frac{x}{6}) = 2 \log (4)$

Step 2

Simplify $2 \log (4)$ by moving $2$ inside the logarithm.

$\log (\frac{x}{6}) = \log (4^{2})$

Step 3

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

$\frac{x}{6} = 4^{2}$

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 \cdot 4^{2}$

Step 4.2

Simplify both sides of the equation.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of $6$ .

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Step 4.2.1.1.1

Cancel the common factor.

$6 \frac{x}{6} = 6 \cdot 4^{2}$

Step 4.2.1.1.2

Rewrite the expression.

$x = 6 \cdot 4^{2}$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Simplify $6 \cdot 4^{2}$ .

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Step 4.2.2.1.1

Raise $4$ to the power of $2$ .

$x = 6 \cdot 16$

Step 4.2.2.1.2

Multiply $6$ by $16$ .

$x = 96$