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Question
If (16)2x+3 =(64)x+3, then 42x-2 =
Options
64
256
32
512
Solution
We have to find the value of`4^(2x -2)`provided `(16)^(2x +3) = (64)^(x+3)`
So,
`(16)^(2x +3) = (64)^(x+3)`
`(2^4)^(2x +3) = (2^6)^(x+3)`
`2^(8x +12) = 2^(6x+18)`
Equating the power of exponents we get
`8x +12 = 6x +18`
`8x - 6x = 18 -12`
`2x = 6`
`x = 6/2`
`x=3`
The value of `4^(2x-2)` is
` = 4^(2x-2)`
`4^(2 xx 3- 2)`
`4^(6-2)`
`4^4`
= 256
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