Question

Solve using properties of logarithm round two decimal places1. 5e^ (-0.4t) = 1.506

Answer 1

To solve the exercise, we can use the following property of logarithms:

`\ln (e^x)=x`

Then, we can solve the equation like this:

`\begin{gathered} 1.5e^(-0.4t)=1.506 \\ \text{ Divide by 1.5 from both sides of the equation} \\ (1.5e^(-0.4t))/(1.5)=(1.506)/(1.5) \\ e^(-0.4t)=1.004 \\ \text{ Apply }\ln \text{ from both sides of the equation} \\ \ln (e^(-0.4t))=\ln (1.004) \\ \text{ Apply the mentioned property of logarithms} \\ -0.4t=\ln (1.004) \\ \text{ Divide by -0.4 from both sides of the equation} \\ (-0.4t)/(-0.4)=(\ln(1.004))/(-0.4) \\ t\approx-0.01\Rightarrow\approx\text{ it reads`

Therefore, the solution of the equation rounded to two decimal places is -0.01.