Precalculus Examples

$\frac{1}{2} \cdot (\log ({(7)}^{s}) + \log ({(7)}^{t}))$

Step 1

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

$\frac{1}{2} \cdot \log ({(7)}^{s} {(7)}^{t})$

Step 2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{2} \cdot \log (7^{s + t})$

Step 3

Simplify $\frac{1}{2} \log (7^{s + t})$ by moving $\frac{1}{2}$ inside the logarithm.

$\log ({(7^{s + t})}^{\frac{1}{2}})$

Step 4

Multiply the exponents in ${(7^{s + t})}^{\frac{1}{2}}$ .

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Step 4.1

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

$\log (7^{(s + t) \frac{1}{2}})$

Step 4.2

Apply the distributive property.

$\log (7^{s \frac{1}{2} + t \frac{1}{2}})$

Step 4.3

Combine $s$ and $\frac{1}{2}$ .

$\log (7^{\frac{s}{2} + t \frac{1}{2}})$

Step 4.4

Combine $t$ and $\frac{1}{2}$ .

$\log (7^{\frac{s}{2} + \frac{t}{2}})$