Rearranging the terms so that the denominator becomes the numerator

Question

I have the equation $$ \frac{120}{1 + 3.167 \cdot e^{-0.05t}} = 60 $$

How do I transform it so that the denominator becomes the numerator? This would make the problem much easier.

Answer 1

Multiply both sides by $1 + 3.167e^{-0.05t}$ to get

$$120 = 60 \cdot (1 + 3.167 e^{-0.05t})$$

Divide both sides by $60$ to get

$$2 = 1 + 3.167 e^{-0.05t}$$

So we have

$$\dfrac{1}{3.167} = e^{-0.05t}$$

Now, solve for $t$, using $\ln$.