Question

Find the value of x when 2^3x = 8^(2x + 1).

Answer 1

x = - 1

Explanation:

using the rule of exponents

•
`(a^m)^(n)` =
`a^(mn)`

given

`2^(3x)` =
`8^((2x+1))` [ note that 8 = 2³ ]

`2^(3x)` =
`(2^3)^((2x+1))`

`2^(3x)` =
`2^((6x+3))`

since bases on both sides are the same, both 2 , then equate exponents

6x + 3 = 3x ( subtract 3x from both sides )

3x + 3 = 0 ( subtract 3 from both sides )

3x = - 3 ( divide both sides by 3 )

x = - 1