Question

4 to the power x minus 4 to the power x minus 1 equal to 24

Answer 1

4X - 4 X-1 = 24
i.e., (2)2x - (2)2(x -1) = 24
i.e., (2)2x - (2)2x -2) = 24
i.e., (2)2x - (2)2x /4= 24

On simplifying, we get
(2)2x = 32 = 25
So, 2x = 5
i.e, x = 5/2
Now,
(2x)x = (2 x 5/2)5/2
= (5)5/2
= 25 (5)1/2
= 25√5

Answer 2

Answer:

$\text{The value of x is }\frac{5}{2}$

Step-by-step explanation:

Given the equation

$4^x-4^{x-1}=24$

we have to find the value of x

$4^x-4^{x-1}=24$

$4^x(1-\frac{1}{4})=24$

$4^x(\frac{3}{4})=24$

$4^x=24\times \frac{4}{3}=32$

$2^{2x}=2^5$

Comparing above

$2x=5$

$x=\frac{5}{2}$

$\text{Hence, the value of x is }\frac{5}{2}$