Precalculus Examples

$\frac{3 \ln (2)}{\ln (5) - \ln (x) + 3 \ln (2)}$

Step 1

Simplify $3 \ln (2)$ by moving $3$ inside the logarithm.

$\frac{\ln (2^{3})}{\ln (5) - \ln (x) + 3 \ln (2)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $3 \ln (2)$ by moving $3$ inside the logarithm.

$\frac{\ln (2^{3})}{\ln (5) - \ln (x) + \ln (2^{3})}$

Step 2.2

Raise $2$ to the power of $3$ .

$\frac{\ln (2^{3})}{\ln (5) - \ln (x) + \ln (8)}$

Step 2.3

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

$\frac{\ln (2^{3})}{\ln (\frac{5}{x}) + \ln (8)}$

Step 2.4

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\ln (2^{3})}{\ln (\frac{5}{x} \cdot 8)}$

Step 2.5

Multiply $\frac{5}{x} \cdot 8$ .

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Step 2.5.1

Combine $\frac{5}{x}$ and $8$ .

$\frac{\ln (2^{3})}{\ln (\frac{5 \cdot 8}{x})}$

Step 2.5.2

Multiply $5$ by $8$ .

$\frac{\ln (2^{3})}{\ln (\frac{40}{x})}$

Step 3

Raise $2$ to the power of $3$ .

$\frac{\ln (8)}{\ln (\frac{40}{x})}$