Basic Math Examples

$90 = 20 \cdot \log (\frac{P}{20})$

Step 1

Rewrite the equation as $20 \cdot \log (\frac{P}{20}) = 90$ .

$20 \cdot \log (\frac{P}{20}) = 90$

Step 2

Divide each term in $20 \cdot \log (\frac{P}{20}) = 90$ by $20$ and simplify.

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Step 2.1

Divide each term in $20 \cdot \log (\frac{P}{20}) = 90$ by $20$ .

$\frac{20 \cdot \log (\frac{P}{20})}{20} = \frac{90}{20}$

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.

$\frac{20 \cdot \log (\frac{P}{20})}{20} = \frac{90}{20}$

Step 2.2.1.2

Divide $\log (\frac{P}{20})$ by $1$ .

$\log (\frac{P}{20}) = \frac{90}{20}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $90$ and $20$ .

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Step 2.3.1.1

Factor $10$ out of $90$ .

$\log (\frac{P}{20}) = \frac{10 (9)}{20}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $10$ out of $20$ .

$\log (\frac{P}{20}) = \frac{10 \cdot 9}{10 \cdot 2}$

Step 2.3.1.2.2

Cancel the common factor.

$\log (\frac{P}{20}) = \frac{10 \cdot 9}{10 \cdot 2}$

Step 2.3.1.2.3

Rewrite the expression.

$\log (\frac{P}{20}) = \frac{9}{2}$

Step 3

Rewrite $\log (\frac{P}{20}) = \frac{9}{2}$ 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 $b^{y} = x$ .

$10^{\frac{9}{2}} = \frac{P}{20}$

Step 4

Solve for $P$ .

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Step 4.1

Rewrite the equation as $\frac{P}{20} = 10^{\frac{9}{2}}$ .

$\frac{P}{20} = 10^{\frac{9}{2}}$

Step 4.2

Multiply both sides of the equation by $20$ .

$20 \frac{P}{20} = 20 \cdot 10^{\frac{9}{2}}$

Step 4.3

Simplify the left side.

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Step 4.3.1

Cancel the common factor of $20$ .

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Step 4.3.1.1

Cancel the common factor.

$20 \frac{P}{20} = 20 \cdot 10^{\frac{9}{2}}$

Step 4.3.1.2

Rewrite the expression.

$P = 20 \cdot 10^{\frac{9}{2}}$

Step 5

The result can be shown in multiple forms.

Scientific Notation:

$P = 20 \cdot 10^{\frac{9}{2}}$

Expanded Form:

$P = 632455.53203367$