Chapter 8.6, Problem 65PPS

To determine

To find: The value of given equation.

Answer to Problem 65PPS

The value of given equation is $y\approx -3.8188$ .

Explanation of Solution

Given information:

The equation is $2^y=\sqrt{3^{y-1}}$ .

Calculation:

Consider the expression.

  $\begin{array}{l}{2}^y=\sqrt{3^{y-1}}\\ 2^y=3^{{\left(y-1\right)}^{0.5}}\\ \log 2^y=\log 3^{{\left(y-1\right)}^{0.5}}\\ y\log 2=\left(0.5y-0.5\right)\log 3\\ \frac{\log 2}{\log 3}=\frac{0.5y-0.5}{y}\\ \frac{\log 2}{\log 3}-0.5=-\frac{0.5}{y}\\ y\approx -3.8188\end{array}$