Algebra Examples

$2 \ln (e) - 4 \ln (1) + 3 \log_{2} (2) + \frac{1}{2} \log_{6} (1)$

Step 1

Simplify each term.

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Step 1.1

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

$2 \cdot 1 - 4 \ln (1) + 3 \log_{2} (2) + \frac{1}{2} \cdot \log_{6} (1)$

Step 1.2

Multiply $2$ by $1$ .

$2 - 4 \ln (1) + 3 \log_{2} (2) + \frac{1}{2} \cdot \log_{6} (1)$

Step 1.3

The natural logarithm of $1$ is $0$ .

$2 - 4 \cdot 0 + 3 \log_{2} (2) + \frac{1}{2} \cdot \log_{6} (1)$

Step 1.4

Multiply $- 4$ by $0$ .

$2 + 0 + 3 \log_{2} (2) + \frac{1}{2} \cdot \log_{6} (1)$

Step 1.5

Logarithm base $2$ of $2$ is $1$ .

$2 + 0 + 3 \cdot 1 + \frac{1}{2} \cdot \log_{6} (1)$

Step 1.6

Multiply $3$ by $1$ .

$2 + 0 + 3 + \frac{1}{2} \cdot \log_{6} (1)$

Step 1.7

Logarithm base $6$ of $1$ is $0$ .

$2 + 0 + 3 + \frac{1}{2} \cdot 0$

Step 1.8

Multiply $\frac{1}{2}$ by $0$ .

$2 + 0 + 3 + 0$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $2$ and $0$ .

$2 + 3 + 0$

Step 2.2

Add $2$ and $3$ .

$5 + 0$

Step 2.3

Add $5$ and $0$ .

$5$