Algebra Examples

$\frac{1}{3} \log (1000) - 2 \log_{2} (64) - \log_{6} (6)$

Step 1

Simplify each term.

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Step 1.1

Logarithm base $10$ of $1000$ is $3$ .

$\frac{1}{3} \cdot 3 - 2 \log_{2} (64) - \log_{6} (6)$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Cancel the common factor.

$\frac{1}{3} \cdot 3 - 2 \log_{2} (64) - \log_{6} (6)$

Step 1.2.2

Rewrite the expression.

$1 - 2 \log_{2} (64) - \log_{6} (6)$

Step 1.3

Logarithm base $2$ of $64$ is $6$ .

$1 - 2 \cdot 6 - \log_{6} (6)$

Step 1.4

Multiply $- 2$ by $6$ .

$1 - 12 - \log_{6} (6)$

Step 1.5

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

$1 - 12 - 1 \cdot 1$

Step 1.6

Multiply $- 1$ by $1$ .

$1 - 12 - 1$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $12$ from $1$ .

$- 11 - 1$

Step 2.2

Subtract $1$ from $- 11$ .

$- 12$