Precalculus Examples

$\frac{1}{3} \cdot (5 - \log (5) \cdot 26)$

Step 1

Multiply $26$ by $- 1$ .

$\frac{1}{3} \cdot (5 - 26 \log (5))$

Step 2

Apply the distributive property.

$\frac{1}{3} \cdot 5 + \frac{1}{3} (- 26 \log (5))$

Step 3

Combine $\frac{1}{3}$ and $5$ .

$\frac{5}{3} + \frac{1}{3} (- 26 \log (5))$

Step 4

Multiply $\frac{1}{3} (- 26 \log (5))$ .

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Step 4.1

Combine $- 26$ and $\frac{1}{3}$ .

$\frac{5}{3} + \frac{- 26}{3} \log (5)$

Step 4.2

Simplify $\frac{- 26}{3} \log (5)$ by moving $- \frac{- 26}{3}$ inside the logarithm.

$\frac{5}{3} - \log (5^{- \frac{- 26}{3}})$

Step 5

Simplify each term.

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Step 5.1

Move the negative in front of the fraction.

$\frac{5}{3} - \log (5^{- - \frac{26}{3}})$

Step 5.2

Multiply $- - \frac{26}{3}$ .

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Step 5.2.1

Multiply $- 1$ by $- 1$ .

$\frac{5}{3} - \log (5^{1 (\frac{26}{3})})$

Step 5.2.2

Multiply $\frac{26}{3}$ by $1$ .

$\frac{5}{3} - \log (5^{\frac{26}{3}})$

Step 6

To write $- \log (5^{\frac{26}{3}})$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3} - \log (5^{\frac{26}{3}}) \cdot \frac{3}{3}$

Step 7

Combine $- \log (5^{\frac{26}{3}})$ and $\frac{3}{3}$ .

$\frac{5}{3} + \frac{- \log (5^{\frac{26}{3}}) \cdot 3}{3}$

Step 8

Simplify the expression.

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Step 8.1

Combine the numerators over the common denominator.

$\frac{5 - \log (5^{\frac{26}{3}}) \cdot 3}{3}$

Step 8.2

Multiply $3$ by $- 1$ .

$\frac{5 - 3 \log (5^{\frac{26}{3}})}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{5 - 3 \log (5^{\frac{26}{3}})}{3}$

Decimal Form:

$- 4.39107337 \dots$