Calculus Examples

$\frac{1}{2} \log (b) + 6 \log (c)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{2} \log (b)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (b^{\frac{1}{2}}) + 6 \log (c)$

Step 1.2

Simplify $6 \log (c)$ by moving $6$ inside the logarithm.

$\log (b^{\frac{1}{2}}) + \log (c^{6})$

Step 2

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

$\log (b^{\frac{1}{2}} c^{6})$

Step 3

Reorder factors in $\log (b^{\frac{1}{2}} c^{6})$ .

$\log (c^{6} b^{\frac{1}{2}})$