Basic Math Examples

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

Step 1

Rewrite $\log (\frac{1}{c}) = 2$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{2} = \frac{1}{c}$

Step 2

Solve for $c$ .

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Step 2.1

Rewrite the equation as $\frac{1}{c} = 10^{2}$ .

$\frac{1}{c} = 10^{2}$

Step 2.2

Raise $10$ to the power of $2$ .

$\frac{1}{c} = 100$

Step 2.3

Find the LCD of the terms in the equation.

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Step 2.3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$c, 1$

Step 2.3.2

The LCM of one and any expression is the expression.

$c$

Step 2.4

Multiply each term in $\frac{1}{c} = 100$ by $c$ to eliminate the fractions.

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Step 2.4.1

Multiply each term in $\frac{1}{c} = 100$ by $c$ .

$\frac{1}{c} c = 100 c$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $c$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{1}{c} c = 100 c$

Step 2.4.2.1.2

Rewrite the expression.

$1 = 100 c$

Step 2.5

Solve the equation.

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Step 2.5.1

Rewrite the equation as $100 c = 1$ .

$100 c = 1$

Step 2.5.2

Divide each term in $100 c = 1$ by $100$ and simplify.

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Step 2.5.2.1

Divide each term in $100 c = 1$ by $100$ .

$\frac{100 c}{100} = \frac{1}{100}$

Step 2.5.2.2

Simplify the left side.

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Step 2.5.2.2.1

Cancel the common factor of $100$ .

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Step 2.5.2.2.1.1

Cancel the common factor.

$\frac{100 c}{100} = \frac{1}{100}$

Step 2.5.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{1}{100}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$c = \frac{1}{100}$

Decimal Form:

$c = 0.01$