Algebra Examples

$\frac{1}{2} \log_{7} (p) + 2 \log_{7} (3)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{1}{2} \log_{7} (p)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{7} (p^{\frac{1}{2}}) + 2 \log_{7} (3)$

Step 1.2

Simplify $2 \log_{7} (3)$ by moving $2$ inside the logarithm.

$\log_{7} (p^{\frac{1}{2}}) + \log_{7} (3^{2})$

Step 1.3

Raise $3$ to the power of $2$ .

$\log_{7} (p^{\frac{1}{2}}) + \log_{7} (9)$

Step 2

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

$\log_{7} (p^{\frac{1}{2}} \cdot 9)$

Step 3

Move $9$ to the left of $p^{\frac{1}{2}}$ .

$\log_{7} (9 p^{\frac{1}{2}})$