Chapter 7.3, Problem 67PPE

To determine

To solve: The equation $5^6={25}^x$ and use the fact if $a^x=a^y$ ,then $x=y$ .

Answer to Problem 67PPE

The required answer is $x=3$ .

Explanation of Solution

Given information:

The given equation $5^6={25}^x$ .

Calculation:

  $\begin{array}{l}\Rightarrow 5^6={25}^x\\ \Rightarrow 5^6=5^{2x}\end{array}$

(Using the fact $a^x=a^y$ )

  $\Rightarrow 6=2x$

(Using $x=y$ )

  $\Rightarrow x=3$

(Simplify)