Basic Math Examples

$\ln (78.5) = 0.0897 t$

Step 1

Rewrite the equation as $0.0897 t = \ln (78.5)$ .

$0.0897 t = \ln (78.5)$

Step 2

Divide each term in $0.0897 t = \ln (78.5)$ by $0.0897$ and simplify.

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Step 2.1

Divide each term in $0.0897 t = \ln (78.5)$ by $0.0897$ .

$\frac{0.0897 t}{0.0897} = \frac{\ln (78.5)}{0.0897}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.0897$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.0897 t}{0.0897} = \frac{\ln (78.5)}{0.0897}$

Step 2.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (78.5)}{0.0897}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Replace $e$ with an approximation.

$t = \frac{\log_{2.71828182} (78.5)}{0.0897}$

Step 2.3.2

Log base $2.71828182$ of $78.5$ is approximately $4.36309862$ .

$t = \frac{4.36309862}{0.0897}$

Step 2.3.3

Divide $4.36309862$ by $0.0897$ .

$t = 48.6410103$