Solve for x 20=20 log of x/200

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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $20$ by $20$ .

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

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 $b^{y} = x$ .

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

Solve for $x$ .

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

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

Multiply both sides of the equation by $200$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $200$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Write $200 \cdot 10^{1}$ in proper scientific notation.

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

The result can be shown in multiple forms.

Scientific Notation:

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

Expanded Form:

$x = 2000$

Solve for x 20=20 log of x/200

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