Algebra Examples

$20 = 20 \log (\frac{x}{200})$

Step 1

Rewrite the equation as $20 \log (\frac{x}{200}) = 20$ .

$20 \log (\frac{x}{200}) = 20$

Step 2

Divide each term in $20 \log (\frac{x}{200}) = 20$ by $20$ and simplify.

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Step 2.1

Divide each term in $20 \log (\frac{x}{200}) = 20$ by $20$ .

$\frac{20 \log (\frac{x}{200})}{20} = \frac{20}{20}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $20$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{20 \log (\frac{x}{200})}{20} = \frac{20}{20}$

Step 2.2.1.2

Divide $\log (\frac{x}{200})$ by $1$ .

$\log (\frac{x}{200}) = \frac{20}{20}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $20$ by $20$ .

$\log (\frac{x}{200}) = 1$

Step 3

Rewrite $\log (\frac{x}{200}) = 1$ 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 $b^{y} = x$ .

$10^{1} = \frac{x}{200}$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $\frac{x}{200} = 10^{1}$ .

$\frac{x}{200} = 10$

Step 4.2

Multiply both sides of the equation by $200$ .

$200 \frac{x}{200} = 200 \cdot 10^{1}$

Step 4.3

Simplify both sides of the equation.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Cancel the common factor of $200$ .

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Step 4.3.1.1.1

Cancel the common factor.

$200 \frac{x}{200} = 200 \cdot 10^{1}$

Step 4.3.1.1.2

Rewrite the expression.

$x = 200 \cdot 10^{1}$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Move the decimal point in $200$ to the left by $2$ places and increase the power of $10^{1}$ by $2$ .

$x = 2 \cdot 10^{3}$

Step 5

The result can be shown in multiple forms.

Scientific Notation:

$x = 2 \cdot 10^{3}$

Expanded Form:

$x = 2000$