Algebra Examples

$\log_{11} (121) + \log_{2} (8^{3}) - 3 \ln (e^{4})$

Step 1

Simplify each term.

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Step 1.1

Logarithm base $11$ of $121$ is $2$ .

$2 + \log_{2} (8^{3}) - 3 \ln (e^{4})$

Step 1.2

Raise $8$ to the power of $3$ .

$2 + \log_{2} (512) - 3 \ln (e^{4})$

Step 1.3

Logarithm base $2$ of $512$ is $9$ .

$2 + 9 - 3 \ln (e^{4})$

Step 1.4

Use logarithm rules to move $4$ out of the exponent.

$2 + 9 - 3 (4 \ln (e))$

Step 1.5

The natural logarithm of $e$ is $1$ .

$2 + 9 - 3 (4 \cdot 1)$

Step 1.6

Multiply $4$ by $1$ .

$2 + 9 - 3 \cdot 4$

Step 1.7

Multiply $- 3$ by $4$ .

$2 + 9 - 12$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $2$ and $9$ .

$11 - 12$

Step 2.2

Subtract $12$ from $11$ .

$- 1$