Precalculus Examples

$0.5 (1 + \log_{9} (x))$

Step 1

Apply the distributive property.

$0.5 \cdot 1 + 0.5 \log_{9} (x)$

Step 2

Multiply $0.5$ by $1$ .

$0.5 + 0.5 \log_{9} (x)$

Step 3

Simplify $0.5 \log_{9} (x)$ by moving $0.5$ inside the logarithm.

$0.5 + \log_{9} (x^{0.5})$

Step 4

Rewrite $\log_{9} (x^{0.5})$ using the change of base formula.

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Step 4.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$0.5 + \log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 4.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$0.5 + \frac{\log (x^{0.5})}{\log (9)}$