Question

Solve the equation by expressing each side as a power of the same base and then equating exponents.

Answer 1

You have the following equation:

4⁽³ˣ⁻⁵⁾ = 256

If you take into account 4=2² and 256 = 2⁸, you can write the previous equation as follow:

2²⁽³ˣ⁻⁵⁾ = 2⁸

Then, you have an equation with two quantities with the same base. It allows you to equal the exponents of both sides and solve for x, just as follow:

2(3x - 5) = 8 apply distribution property left side

2(3x) - 2(5) = 8

6x - 10 = 8 add 10 both sides

6x = 8 + 10 simplify

6x = 18 divide both sides by 6

x = 18/6

x = 3

Hence, the solution for x is x = 3