Chapter 3.2, Problem 76E

To determine

To rewrite:

The given exponentialequation in logarithmic form.

Answer to Problem 76E

The given exponential equation in logarithmicform would be $\ln \left(\mathrm{2.1170...}\right)=\frac{3}{4}$.

Explanation of Solution

Given:

Anexponential equation: $e^{\frac{3}{4}}=\mathrm{2.1170...}$

Concept used:

In order to change anexponential equation into logarithmic form, we can use the formula $e^a=c\Rightarrow a=\ln \left(c\right)$.

Calculation:

We can see that the value of c is $\mathrm{2.1170...}$ and the value of a is $\frac{3}{4}$ in our given question.

Upon applying conversion formula for exponential form to natural log, we will get:

  $e^{\frac{3}{4}}=\mathrm{2.1170...}\Rightarrow \ln \left(\mathrm{2.1170...}\right)=\frac{3}{4}$

Therefore, the given exponential equation in logarithmic form would be $\ln \left(\mathrm{2.1170...}\right)=\frac{3}{4}$ .