Precalculus Examples

$\log_{5} (625 \cdot e^{2 \ln (5)}) + 3 \cdot 2^{\log_{2} (3)}$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \ln (5)$ by moving $2$ inside the logarithm.

$\log_{5} (625 \cdot e^{\ln (5^{2})}) + 3 \cdot 2^{\log_{2} (3)}$

Step 1.2

Exponentiation and log are inverse functions.

$\log_{5} (625 \cdot 5^{2}) + 3 \cdot 2^{\log_{2} (3)}$

Step 1.3

Raise $5$ to the power of $2$ .

$\log_{5} (625 \cdot 25) + 3 \cdot 2^{\log_{2} (3)}$

Step 1.4

Multiply $625$ by $25$ .

$\log_{5} (15625) + 3 \cdot 2^{\log_{2} (3)}$

Step 1.5

Logarithm base $5$ of $15625$ is $6$ .

$6 + 3 \cdot 2^{\log_{2} (3)}$

Step 1.6

Exponentiation and log are inverse functions.

$6 + 3 \cdot 3$

Step 1.7

Multiply $3$ by $3$ .

$6 + 9$

Step 2

Add $6$ and $9$ .

$15$