Basic Math Examples

$0.0016 = 4^{- 0.056 t}$

Step 1

Rewrite the equation as $4^{- 0.056 t} = 0.0016$ .

$4^{- 0.056 t} = 0.0016$

Step 2

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

$\ln (4^{- 0.056 t}) = \ln (0.0016)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (4^{- 0.056 t})$ by moving $- 0.056 t$ outside the logarithm.

$- 0.056 t \ln (4) = \ln (0.0016)$

Step 3.2

Multiply $\ln (4)$ by $- 0.056$ .

$- 0.07763248 t = \ln (0.0016)$

Step 4

Divide each term in $- 0.07763248 t = \ln (0.0016)$ by $- 0.07763248$ and simplify.

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Step 4.1

Divide each term in $- 0.07763248 t = \ln (0.0016)$ by $- 0.07763248$ .

$\frac{- 0.07763248 t}{- 0.07763248} = \frac{\ln (0.0016)}{- 0.07763248}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 0.07763248$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 0.07763248 t}{- 0.07763248} = \frac{\ln (0.0016)}{- 0.07763248}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (0.0016)}{- 0.07763248}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$t = - \frac{\ln (0.0016)}{0.07763248}$

Step 4.3.2

Replace $e$ with an approximation.

$t = - \frac{\log_{2.71828182} (0.0016)}{0.07763248}$

Step 4.3.3

Log base $2.71828182$ of $0.0016$ is approximately $- 6.43775164$ .

$t = - \frac{- 6.43775164}{0.07763248}$

Step 4.3.4

Divide $- 6.43775164$ by $0.07763248$ .

$t = - - 82.92600338$

Step 4.3.5

Multiply $- 1$ by $- 82.92600338$ .

$t = 82.92600338$