Trigonometry Examples

$\log (\frac{x}{100}) = 6$

Step 1

Rewrite $\log (\frac{x}{100}) = 6$ 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 $b^{y} = x$ .

$10^{6} = \frac{x}{100}$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $\frac{x}{100} = 10^{6}$ .

$\frac{x}{100} = 10^{6}$

Step 2.2

Multiply both sides of the equation by $100$ .

$100 \frac{x}{100} = 100 \cdot 10^{6}$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of $100$ .

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Step 2.3.1.1.1

Cancel the common factor.

$100 \frac{x}{100} = 100 \cdot 10^{6}$

Step 2.3.1.1.2

Rewrite the expression.

$x = 100 \cdot 10^{6}$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $100 \cdot 10^{6}$ .

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Step 2.3.2.1.1

Move the decimal point in $100$ to the left by $2$ places and increase the power of $10^{6}$ by $2$ .

$x = 1 \cdot 10^{8}$

Step 2.3.2.1.2

Multiply $10^{8}$ by $1$ .

$x = 10^{8}$

Step 2.3.2.1.3

Raise $10$ to the power of $8$ .

$x = 100000000$