Chapter 11.6, Problem 44E

To determine

The value of given inequality by using natural logarithms.

Answer to Problem 44E

The value of the given inequality is $42.917<y$ .

Explanation of Solution

Given:

  $25<e^{0.075y}$

Solution:

From the given equation,

  $\begin{array}{l}25<e^{0.075y}\\ \ln 25<\ln e^{0.075y}\left(\text{taking}\text{natural}\text{log}\right)\\ 3.2188<0.075y\ln e\left(\ln a^x=x\ln a\right)\\ 3.2188<0.075y\\ \frac{3.2188}{0.075}<y\\ 2.968t<1\\ 42.917<y\end{array}$

The value of the given inequality is $42.917<y$ .