Precalculus Examples

$\log_{7} (7) + \log_{7} (49) + 3^{\log_{3} (7)}$

Step 1

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

$\log_{7} (7 \cdot 49) + 3^{\log_{3} (7)}$

Step 2

Simplify each term.

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Step 2.1

Multiply $7$ by $49$ .

$\log_{7} (343) + 3^{\log_{3} (7)}$

Step 2.2

Logarithm base $7$ of $343$ is $3$ .

$3 + 3^{\log_{3} (7)}$

Step 2.3

Exponentiation and log are inverse functions.

$3 + 7$

Step 3

Add $3$ and $7$ .

$10$