Chapter 16, Problem 1RE

To determine

To solve: The equation $5^x=5^8$.

Answer to Problem 1RE

The solution of the equation $5^x=5^8$ is $\underset{\_}{x=8}$.

Explanation of Solution

Procedure used:

To solve an exponential equation in the form of $b^x=b^y$:

1. If the given equation is not in the form of $b^x=b^y$, then rewrite it in the above form.

2. For solving x, if $b^x=b^y,b>0\text{ and }b\ne 1$ then $x=y$ where x and y are real numbers.

Calculation:

The given equation is $5^x=5^8$.

It is observed that the given equation is in the form of $b^x=b^y$.

Here $b=5$ satisfies the conditions of $5>0\text{ and 5}\ne 1$.

Then the solution will be $x=y$.

That is, $x=8$.

Thus, by the above procedure the solution of the equation $5^x=5^8$ is $\underset{\_}{x=8}$.