Precalculus Examples

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

Step 1

Exponentiation and log are inverse functions.

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

Step 2

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

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

Step 3

Multiply $625$ by $25$ .

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

Step 4

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

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

Step 5

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

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

Step 6

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

$6 + 3 \cdot \log_{2} (9)$

Step 7

Simplify $3 \log_{2} (9)$ by moving $3$ inside the logarithm.

$6 + \log_{2} (9^{3})$

Step 8

Raise $9$ to the power of $3$ .

$6 + \log_{2} (729)$

Step 9

The result can be shown in multiple forms.

Exact Form:

$6 + \log_{2} (729)$

Decimal Form:

$15.50977500 \dots$