Precalculus Examples

$\frac{1}{2} \cdot (\log_{4} (s) + \log_{4} (t))$

Step 1

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

$\frac{1}{2} \cdot \log_{4} (s t)$

Step 2

Simplify $\frac{1}{2} \log_{4} (s t)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{4} ({(s t)}^{\frac{1}{2}})$

Step 3

Apply the product rule to $s t$ .

$\log_{4} (s^{\frac{1}{2}} t^{\frac{1}{2}})$

Step 4

Rewrite $\log_{4} (s^{\frac{1}{2}} t^{\frac{1}{2}})$ 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 $0$ .

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

Step 4.2

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

$\frac{\log (s^{\frac{1}{2}} t^{\frac{1}{2}})}{\log (4)}$