Question

32^{3x+5}=8^{x−1} I need help plz

Answer 1

Answer:

The value of x for the given expression is $\dfrac{- 7}{3}$

Step-by-step 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 = $\dfrac{- 7}{3}$

So, The value of x = $\dfrac{- 7}{3}$

Hence, The value of x for the given expression is $\dfrac{- 7}{3}$ Answer