Algebra Examples

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

Step 1

Multiply $7^{3}$ by $7^{8}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2

Add $3$ and $8$ .

$\log_{7} (7^{11})$

Step 2

Use logarithm rules to move $11$ out of the exponent.

$11 \log_{7} (7)$

Step 3

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

$11 \cdot 1$

Step 4

Multiply $11$ by $1$ .

$11$