Basic Math Examples

$\ln (p) = \ln (105000) + 0.55 \cdot 50$

Step 1

Simplify the right side.

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Step 1.1

Multiply $0.55$ by $50$ .

$\ln (p) = \ln (105000) + 27.5$

Step 2

Move all the terms containing a logarithm to the left side of the equation.

$\ln (p) - \ln (105000) = 27.5$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{p}{105000}) = 27.5$

Step 4

To solve for $p$ , rewrite the equation using properties of logarithms.

$e^{\ln (\frac{p}{105000})} = e^{27.5}$

Step 5

Rewrite $\ln (\frac{p}{105000}) = 27.5$ 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 $b^{y} = x$ .

$e^{27.5} = \frac{p}{105000}$

Step 6

Solve for $p$ .

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Step 6.1

Rewrite the equation as $\frac{p}{105000} = e^{27.5}$ .

$\frac{p}{105000} = e^{27.5}$

Step 6.2

Multiply both sides of the equation by $105000$ .

$105000 \frac{p}{105000} = 105000 e^{27.5}$

Step 6.3

Simplify the left side.

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Step 6.3.1

Cancel the common factor of $105000$ .

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Step 6.3.1.1

Cancel the common factor.

$105000 \frac{p}{105000} = 105000 e^{27.5}$

Step 6.3.1.2

Rewrite the expression.

$p = 105000 e^{27.5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$p = 105000 e^{27.5}$

Decimal Form:

$p = 9.21059213 \cdot 10^{16}$