Precalculus Examples

$\frac{\log (x + 7)}{\log (6)} = 2$

Step 1

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

$\log (6) \frac{\log (x + 7)}{\log (6)} = \log (6) \cdot 2$

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.

$\log (6) \frac{\log (x + 7)}{\log (6)} = \log (6) \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$\log (x + 7) = \log (6) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Move $2$ to the left of $\log (6)$ .

$\log (x + 7) = 2 \log (6)$

Step 3

Simplify $2 \log (6)$ by moving $2$ inside the logarithm.

$\log (x + 7) = \log (6^{2})$

Step 4

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

$x + 7 = 6^{2}$

Step 5

Solve for $x$ .

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Step 5.1

Raise $6$ to the power of $2$ .

$x + 7 = 36$

Step 5.2

Move all terms not containing $x$ to the right side of the equation.

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Step 5.2.1

Subtract $7$ from both sides of the equation.

$x = 36 - 7$

Step 5.2.2

Subtract $7$ from $36$ .

$x = 29$