Question

lf 4 to the power x - 4 to the power x-1 then find the value of X​

Answer 1

4^x-4^x-1=24

4^x-4^x × 4^-1=24

4^x (1-4^-1)=24

4^x (1-1÷4)=24

(taking LCM)

4^x (4-1÷4)=24

4^x (3÷4)=24

4^x=24×4÷3

(on solving 24÷3 =8)

4^x=8×4÷1

4^x=32

(2^2)^x=2^5

2^2x=2^5

Sice the bases are same we equate the powers,therefore

2x=5

x=5÷2

So the answer is 5÷2 or 2.5

Answer 2

Step-by-step explanation:

4^x-4^x-1=24

4^x-4^x × 4^-1=24

4^x (1-4^-1)=24

4^x (1-1÷4)=24

(taking LCM)

4^x (4-1÷4)=24

4^x (3÷4)=24

4^x=24×4÷3

(on solving 24÷3 =8)

4^x=8×4÷1

4^x=32

(2^2)^x=2^5

2^2x=2^5

Since the bases are same we equate the powers,therefore

2x=5

x=5÷2

So the answer is 5÷2 or 2.5

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