Question

plz answer the question

If 4x - 4x-¹ = 24, then find the value of x.​

Answer 1

Answer:   2.5

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

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:

${4}^{x} - {4}^{x - 1} = 24 \\ \implies \: {4}^{x} - ( \frac{ {4}^{x} }{4} ) = 24 \\ \implies \: {4}^{x} (1 - \frac{1}{4} ) = 24 \\ \implies {4}^{x} ( \frac{4 - 1}{4} ) = 24 \\ \implies \: {4}^{x} \times \frac{3}{4} = 24 \\ \implies \: {4}^{x} = 24 \times \frac{4}{3} \\ \implies {4}^{x} = 32 \\ \implies {4}^{x} = {2}^{5} \\ \implies {2}^{2x} = {2}^{5} \\ \implies2x = 5 \\ \implies \: x = \frac{5}{2}$