Finite Math Examples

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

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

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}

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

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

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

Step 1.2

Subtract

{0.2}^{- x}

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

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

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

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

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

Step 2

Move

- {0.2}^{- x}

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

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

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

Step 3

Take the log of both sides of the equation.

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

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

Step 4

Expand

ln ({7.1}^{x})

$\ln ({7.1}^{x})$ by moving

x

$x$ outside the logarithm.

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

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

Step 5

Expand

ln ({0.2}^{- x})

$\ln ({0.2}^{- x})$ by moving

- x

$- x$ outside the logarithm.

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

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

Step 6

Solve the equation for

x

$x$ .

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Step 6.1

Add

x ln (0.2)

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

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

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

Step 6.2

Factor

x

$x$ out of

x ln (7.1) + x ln (0.2)

$x \ln (7.1) + x \ln (0.2)$ .

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Step 6.2.1

Factor

x

$x$ out of

x ln (7.1)

$x \ln (7.1)$ .

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

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

Step 6.2.2

Factor

x

$x$ out of

x ln (0.2)

$x \ln (0.2)$ .

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

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

Step 6.2.3

Factor

x

$x$ out of

x (ln (7.1)) + x (ln (0.2))

$x (\ln (7.1)) + x (\ln (0.2))$ .

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

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

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

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

Step 6.3

Divide each term in

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

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

ln (7.1) + ln (0.2)

$\ln (7.1) + \ln (0.2)$ and simplify.

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Step 6.3.1

Divide each term in

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

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

ln (7.1) + ln (0.2)

$\ln (7.1) + \ln (0.2)$ .

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

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

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)

$\ln (7.1) + \ln (0.2)$ .

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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)}

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

Step 6.3.2.1.2

Divide

x

$x$ by

1

$1$ .

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

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

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

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

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

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

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Divide

0

$0$ by

ln (7.1) + ln (0.2)

$\ln (7.1) + \ln (0.2)$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$