Finite Math Examples

$10000 = 1500 x^{0.09 y}$

Step 1

Rewrite the equation as $1500 x^{0.09 y} = 10000$ .

$1500 x^{0.09 y} = 10000$

Step 2

Divide each term in $1500 x^{0.09 y} = 10000$ by $1500$ and simplify.

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Step 2.1

Divide each term in $1500 x^{0.09 y} = 10000$ by $1500$ .

$\frac{1500 x^{0.09 y}}{1500} = \frac{10000}{1500}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $1500$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{1500 x^{0.09 y}}{1500} = \frac{10000}{1500}$

Step 2.2.1.2

Divide $x^{0.09 y}$ by $1$ .

$x^{0.09 y} = \frac{10000}{1500}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $10000$ and $1500$ .

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Step 2.3.1.1

Factor $500$ out of $10000$ .

$x^{0.09 y} = \frac{500 (20)}{1500}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $500$ out of $1500$ .

$x^{0.09 y} = \frac{500 \cdot 20}{500 \cdot 3}$

Step 2.3.1.2.2

Cancel the common factor.

$x^{0.09 y} = \frac{500 \cdot 20}{500 \cdot 3}$

Step 2.3.1.2.3

Rewrite the expression.

$x^{0.09 y} = \frac{20}{3}$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (x^{0.09 y}) = \ln (\frac{20}{3})$

Step 4

Expand $\ln (x^{0.09 y})$ by moving $0.09 y$ outside the logarithm.

$0.09 y \ln (x) = \ln (\frac{20}{3})$

Step 5

Divide each term in $0.09 y \ln (x) = \ln (\frac{20}{3})$ by $0.09 \ln (x)$ and simplify.

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Step 5.1

Divide each term in $0.09 y \ln (x) = \ln (\frac{20}{3})$ by $0.09 \ln (x)$ .

$\frac{0.09 y \ln (x)}{0.09 \ln (x)} = \frac{\ln (\frac{20}{3})}{0.09 \ln (x)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $0.09$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{0.09 y \ln (x)}{0.09 \ln (x)} = \frac{\ln (\frac{20}{3})}{0.09 \ln (x)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{y \ln (x)}{\ln (x)} = \frac{\ln (\frac{20}{3})}{0.09 \ln (x)}$

Step 5.2.2

Cancel the common factor of $\ln (x)$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{y \ln (x)}{\ln (x)} = \frac{\ln (\frac{20}{3})}{0.09 \ln (x)}$

Step 5.2.2.2

Divide $y$ by $1$ .

$y = \frac{\ln (\frac{20}{3})}{0.09 \ln (x)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply by $1$ .

$y = \frac{1 \ln (\frac{20}{3})}{0.09 \ln (x)}$

Step 5.3.2

Factor $0.09$ out of $0.09 \ln (x)$ .

$y = \frac{1 \ln (\frac{20}{3})}{0.09 \ln (x)}$

Step 5.3.3

Separate fractions.

$y = \frac{1}{0.09} \cdot \frac{\ln (\frac{20}{3})}{\ln (x)}$

Step 5.3.4

Divide $1$ by $0.09$ .

$y = 11.\overline{1} \frac{\ln (\frac{20}{3})}{\ln (x)}$

Step 5.3.5

Combine $11.\overline{1}$ and $\frac{\ln (\frac{20}{3})}{\ln (x)}$ .

$y = \frac{11.\overline{1} \ln (\frac{20}{3})}{\ln (x)}$