Precalculus Examples

$4^{- x} = 2.8$

Step 1

Subtract $2.8$ from both sides of the equation.

$4^{- x} - 2.8 = 0$

Step 2

Add $2.8$ to both sides of the equation.

$4^{- x} = 2.8$

Step 3

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

$\ln (4^{- x}) = \ln (2.8)$

Step 4

Expand $\ln (4^{- x})$ by moving $- x$ outside the logarithm.

$- x \ln (4) = \ln (2.8)$

Step 5

Divide each term in $- x \ln (4) = \ln (2.8)$ by $- \ln (4)$ and simplify.

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Step 5.1

Divide each term in $- x \ln (4) = \ln (2.8)$ by $- \ln (4)$ .

$\frac{- x \ln (4)}{- \ln (4)} = \frac{\ln (2.8)}{- \ln (4)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (2.8)}{- \ln (4)}$

Step 5.2.2

Cancel the common factor of $\ln (4)$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (2.8)}{- \ln (4)}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (2.8)}{- \ln (4)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x = - \frac{\ln (2.8)}{\ln (4)}$