Chapter 7.3, Problem 5AGP

To determine

To solve the given equation.

Answer to Problem 5AGP

  $x=3$

Explanation of Solution

Given:

Equation: $5^x=125$

Formula used:

Exponent rules:

  ${(a^b)}^c=a^{bc}$

  $a^{f(x)}=a^{g(x)},$ then $f(x)=g(x)$

Distributive property: $a(b+c)=a\cdot b+a\cdot c$

Calculation:

Consider the given equation,

  $5^x=125$

Here, 125 can be written as $5^3.$

Hence,

  $\begin{array}{c}{5}^x=5^3\\ x=3[\because a^{f(x)}=a^{g(x)},\text{then }f(x)=g(x)]\end{array}$

Conclusion:

Therefore, the solution to the given equation is $x=3.$