Question

find solution of equation 3.2^ x /2 - 7.2^ x /4 = 20

Answer 1

Given, $\bold{3.2^{x/2}-7.2^{x/4}=20}$
Let , $\bold{2^{x/4}}$ = P
Then, 3.(P)² - 7P = 20
⇒3p² - 7P - 20 = 0
⇒3P² - 12P + 5P - 20 = 0
⇒3P(P - 4) + 5(P - 4) = 0
⇒(3P + 5)(P - 4) = 0
⇒P = 4 and -5/3

But we know, exponential function doesn't negative
So, P = $\bold{2^{x/4}}$ ≠ -5/3
∴ P = $\bold{2^{x/4}}$ = 4
⇒$\bold{2^{x/4}}$ = 2²
⇒x/4 = 2
⇒x = 8

Hence, answer is 8