Calculus Examples

$\ln (y - 40) = 5 t$

Step 1

To solve for $y$ , rewrite the equation using properties of logarithms.

$e^{\ln (y - 40)} = e^{5 t}$

Step 2

Rewrite $\ln (y - 40) = 5 t$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{5 t} = y - 40$

Step 3

Solve for $y$ .

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Step 3.1

Rewrite the equation as $y - 40 = e^{5 t}$ .

$y - 40 = e^{5 t}$

Step 3.2

Add $40$ to both sides of the equation.

$y = e^{5 t} + 40$