Chapter 7.2, Problem 44HP

Solution

To find: Whether the given statement is correct or not.

The value of the given statement is $x=\left(\frac{\log 5}{\log 4}\right)+32$ .

Given information: The given statement is $6^{18}+6^{18}+6^{18}+6^{18}+6^{18}=4^x$ .

Explanation: Consider $6^{18}+6^{18}+6^{18}+6^{18}+6^{18}=4^x$ .

Solve the given statement.

  $\begin{array}{c}5\left(4^{2\left(18\right)}\right)=4^x\\ 5\left(4^{32}\right)=4^x\\ 5=\frac{4^x}{4^{32}}\\ 5=4^{\left(x-32\right)}\end{array}$

Taking $\log$ on both sides,

  $\begin{array}{c}\log 5=\left(x-32\right)\log 4\\ x=\left(\frac{\log 5}{\log 4}\right)+32\end{array}$

Therefore, the value of the statement is $x=\left(\frac{\log 5}{\log 4}\right)+32$ .