Answer:
The value of x for the given expression is [tex]\dfrac{- 7}{3}[/tex]
Step-by-step explanation:
Given as :
The expression is
[tex](32)^{3 x + 5}[/tex] = [tex](8)^{ x - 1}[/tex]
Now,
∵ [tex](2)^{5}[/tex] = 32
And [tex](2)^{3}[/tex] = 8
So, [tex](2^{5})^{3 x + 5}[/tex] = [tex](2^{3})^{x - 1}[/tex]
Or, [tex]2^{15 x + 25}[/tex] = [tex]2^{3 x - 3}[/tex]
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 = [tex]\dfrac{- 7}{3}[/tex]
So, The value of x = [tex]\dfrac{- 7}{3}[/tex]
Hence, The value of x for the given expression is [tex]\dfrac{- 7}{3}[/tex] Answer
