Basic Math Examples

$\frac{\log (2)}{\log (\frac{1}{2})} = c$

Step 1

Rewrite the equation as $c = \frac{\log (2)}{\log (\frac{1}{2})}$ .

$c = \frac{\log (2)}{\log (\frac{1}{2})}$

Step 2

Simplify $\frac{\log (2)}{\log (\frac{1}{2})}$ .

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Step 2.1

Rewrite $\frac{1}{2}$ as $2^{- 1}$ .

$c = \frac{\log (2)}{\log (2^{- 1})}$

Step 2.2

Expand $\log (2^{- 1})$ by moving $- 1$ outside the logarithm.

$c = \frac{\log (2)}{- \log (2)}$

Step 2.3

Cancel the common factor of $\log (2)$ .

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Step 2.3.1

Cancel the common factor.

$c = \frac{\log (2)}{- \log (2)}$

Step 2.3.2

Rewrite the expression.

$c = \frac{1}{- 1}$

Step 2.3.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$c = - 1 \cdot 1$

Step 2.4

Multiply $- 1$ by $1$ .

$c = - 1$