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

$8$ .

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

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

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

$1$ .

$11$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$