Question

32^{3x+5}=8^{x−1} I need help plz

Answer 1

The value of x for the given expression is
`(- 7)/(3)`

Explanation:

Given as :

The expression is

`(32)^(3 x + 5)` =
`(8)^( x - 1)`

Now,

∵
`(2)^(5)` = 32

And
`(2)^(3)` = 8

So,
`(2^(5))^(3 x + 5)` =
`(2^(3))^(x - 1)`

Or,
`2^(15 x + 25)` =
`2^(3 x - 3)`

Here , on both side base is 2 , so we remove common base 2

∴ Equation can be written as

15 x + 25 = 3 x - 3

Or, 15 x - 3 x = - 25 - 3

Or, 12 x = - 28

∴ x =
`(- 7)/(3)`

So, The value of x =
`(- 7)/(3)`

Hence, The value of x for the given expression is
`(- 7)/(3)` Answer