Precalculus Examples

$\frac{1}{4} \cdot \log (81) + \log (6) - \log (5)$

Step 1

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

$\frac{1}{4} \cdot \log (81) + \log (\frac{6}{5})$

Step 2

Simplify each term.

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Step 2.1

Simplify $\frac{1}{4} \log (81)$ by moving $\frac{1}{4}$ inside the logarithm.

$\log (81^{\frac{1}{4}}) + \log (\frac{6}{5})$

Step 2.2

Rewrite $81$ as $3^{4}$ .

$\log ({(3^{4})}^{\frac{1}{4}}) + \log (\frac{6}{5})$

Step 2.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (3^{4 (\frac{1}{4})}) + \log (\frac{6}{5})$

Step 2.4

Cancel the common factor of $4$ .

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Step 2.4.1

Cancel the common factor.

$\log (3^{4 (\frac{1}{4})}) + \log (\frac{6}{5})$

Step 2.4.2

Rewrite the expression.

$\log (3^{1}) + \log (\frac{6}{5})$

Step 2.5

Evaluate the exponent.

$\log (3) + \log (\frac{6}{5})$

Step 3

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

$\log (3 (\frac{6}{5}))$

Step 4

Multiply $3 (\frac{6}{5})$ .

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Step 4.1

Combine $3$ and $\frac{6}{5}$ .

$\log (\frac{3 \cdot 6}{5})$

Step 4.2

Multiply $3$ by $6$ .

$\log (\frac{18}{5})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{18}{5})$

Decimal Form:

$0.55630250 \dots$