Finite Math Examples

${7.1}^{x} = {(0.2)}^{- x}$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the right side.

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Step 1.1.1

Remove parentheses.

${7.1}^{x} = {0.2}^{- x}$

Step 1.2

Subtract ${0.2}^{- x}$ from both sides of the equation.

${7.1}^{x} - {0.2}^{- x} = 0$

Step 2

Move $- {0.2}^{- x}$ to the right side of the equation by adding it to both sides.

${7.1}^{x} = {0.2}^{- x}$

Step 3

Take the log of both sides of the equation.

$\ln ({7.1}^{x}) = \ln ({0.2}^{- x})$

Step 4

Expand $\ln ({7.1}^{x})$ by moving $x$ outside the logarithm.

$x \ln (7.1) = \ln ({0.2}^{- x})$

Step 5

Expand $\ln ({0.2}^{- x})$ by moving $- x$ outside the logarithm.

$x \ln (7.1) = - x \ln (0.2)$

Step 6

Solve the equation for $x$ .

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Step 6.1

Add $x \ln (0.2)$ to both sides of the equation.

$x \ln (7.1) + x \ln (0.2) = 0$

Step 6.2

Factor $x$ out of $x \ln (7.1) + x \ln (0.2)$ .

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Step 6.2.1

Factor $x$ out of $x \ln (7.1)$ .

$x (\ln (7.1)) + x \ln (0.2) = 0$

Step 6.2.2

Factor $x$ out of $x \ln (0.2)$ .

$x (\ln (7.1)) + x (\ln (0.2)) = 0$

Step 6.2.3

Factor $x$ out of $x (\ln (7.1)) + x (\ln (0.2))$ .

$x (\ln (7.1) + \ln (0.2)) = 0$

Step 6.3

Divide each term in $x (\ln (7.1) + \ln (0.2)) = 0$ by $\ln (7.1) + \ln (0.2)$ and simplify.

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Step 6.3.1

Divide each term in $x (\ln (7.1) + \ln (0.2)) = 0$ by $\ln (7.1) + \ln (0.2)$ .

$\frac{x (\ln (7.1) + \ln (0.2))}{\ln (7.1) + \ln (0.2)} = \frac{0}{\ln (7.1) + \ln (0.2)}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $\ln (7.1) + \ln (0.2)$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{x (\ln (7.1) + \ln (0.2))}{\ln (7.1) + \ln (0.2)} = \frac{0}{\ln (7.1) + \ln (0.2)}$

Step 6.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{\ln (7.1) + \ln (0.2)}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Divide $0$ by $\ln (7.1) + \ln (0.2)$ .

$x = 0$