Algebra Examples

$\log_{7} (7^{3} \cdot 7^{8})$

Step 1

Rewrite $\log_{7} (7^{3} \cdot 7^{8})$ as $\log_{7} (7^{3}) + \log_{7} (7^{8})$ .

$\log_{7} (7^{3}) + \log_{7} (7^{8})$

Step 2

Expand $\log_{7} (7^{3})$ by moving $3$ outside the logarithm.

$3 \log_{7} (7) + \log_{7} (7^{8})$

Step 3

Expand $\log_{7} (7^{8})$ by moving $8$ outside the logarithm.

$3 \log_{7} (7) + 8 \log_{7} (7)$

Step 4

Logarithm base $7$ of $7$ is $1$ .

$3 \cdot 1 + 8 \log_{7} (7)$

Step 5

Logarithm base $7$ of $7$ is $1$ .

$3 \cdot 1 + 8 \cdot 1$

Step 6

Multiply $3$ by $1$ .

$3 + 8 \cdot 1$

Step 7

Multiply $8$ by $1$ .

$3 + 8$

Step 8

Add $3$ and $8$ .

$11$