Precalculus Examples

$\frac{6}{\frac{\log (15)}{\log (5)}} + 1$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply the numerator by the reciprocal of the denominator.

$6 \frac{\log (5)}{\log (15)} + 1$

Step 1.1.2

Multiply $6 \frac{\log (5)}{\log (15)}$ .

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Step 1.1.2.1

Combine $6$ and $\frac{\log (5)}{\log (15)}$ .

$\frac{6 \log (5)}{\log (15)} + 1$

Step 1.1.2.2

Simplify $6 \log (5)$ by moving $6$ inside the logarithm.

$\frac{\log (5^{6})}{\log (15)} + 1$

Step 1.1.3

Raise $5$ to the power of $6$ .

$\frac{\log (15625)}{\log (15)} + 1$

Step 1.2

Simplify the expression.

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{\log (15625)}{\log (15)} + \frac{\log (15)}{\log (15)}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{\log (15625) + \log (15)}{\log (15)}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{\log (15625 \cdot 15)}{\log (15)}$

Step 2.2

Multiply $15625$ by $15$ .

$\frac{\log (234375)}{\log (15)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (234375)}{\log (15)}$

Decimal Form:

$4.56589677 \dots$