Question

If 10^3x= 10 ^ (x-8), solve for x. Be sure to check your answer.

Answer 1

x = - 4

Explanation:

given

`10^(3x)` =
`10^(x-8)`

since the bases on both sides are equal, both 10 , then equate the exponents , that is

3x = x - 8 ( subtract x from both sides )

2x = - 8 ( divide both sides by 2 )

x = - 4

as a check

substitute x = - 4 into both sides of the equation

left side =
`10^(3(-4))` =
`10^(-12)`

right side =
`10^(-4-8)` =
`10^(-12)`

both sides are equal , then the solution is x = - 4