Question

$4 {}^{x} - 4 {}^{x - 1} = 24$
Answer it​

Answer 1

Answer:

x = 5 / 2

Step-by-step explanation:

Given-----> 4ˣ - 4ˣ⁻¹ = 24

To find-----> ATQ,

4ˣ - 4ˣ⁻¹ =24

We know that,

aᵐ⁻ⁿ = aᵐ a⁻ⁿ , applying it here, we get,

=> 4ˣ - 4ˣ 4⁻¹ = 24

Taking 4ˣ , common , we get,

=> 4ˣ ( 1 - 4⁻¹ ) = 24

=> 4ˣ { 1 - ( 1 / 4 ) } = 24

=> 4ˣ { ( 4 - 1 ) / 4 } = 24

=> 4ˣ ( 3 / 4 ) = 24

=> 4ˣ = 24 × 4 / 3

=> 4ˣ = 8 × 4

=> ( 2² )ˣ = 32

=> 2²ˣ = 2⁵

Comparing the exponent , we get,

=> 2x = 5

=> x = 5 / 2