Chapter SH, Problem 7.3EP

To determine

To find:the solution of the equation.

Answer to Problem 7.3EP

  $\text{x=-5}$ .

Explanation of Solution

Given:

  ${\text{2}}^{\text{x-1}}{\text{=8}}^{\text{x+3}}$ .

Concept used:

If the base of the left hands side and right hands side are equal then power can be compared to each to get the solution.

larger number can be abbreviatedto smaller by using exponential operator.

Calculation:

Here the given equation:

  ${\text{2}}^{\text{x-1}}{\text{=8}}^{\text{x+3}}$ .

  ${\text{2}}^{\text{x-1}}\text{=}{\left(\text{2}\right)}^{\text{3}}{}^{\left(\text{x+3}\right)}$ .

Comparing he power:

  $\text{x-1=3}\left(\text{x+3}\right)$ .

  $\text{x-1=3x+9}$ .

  $\text{-2x=10}$ .

Dividing both side by $\text{-2}$ :

  $\text{x=-5}$ .

Hence, $\text{x=-5}$ .