Question

Please solve this Question !​

Answer 1

Given---> 4ˣ - 4ˣ⁻¹ = 24

To find ---> Value of x

Solution--->

4ˣ - 4ˣ⁻¹ = 24

We have a law of exponent as follows

aᵐ⁻ⁿ = aᵐ a⁻ⁿ

Applying it we get

=> 4ˣ - 4ˣ 4⁻¹ = 24

Taking out 4ˣ as common from LHS of given equation

=> 4ˣ ( 1 - 4⁻¹ ) = 24

=> 4ˣ ( 1 - 1/4 )= 24

Taking 4 as LCM

=> 4ˣ {( 4 - 1 ) / 4} = 24

=> 4ˣ ( 3 / 4 ) = 24

=> 4ˣ = (4 × 24 ) / 3

=> 4ˣ = 32

=> ( 2 × 2 )ˣ = 2 × 2 × 2 × 2 × 2

We have a law of exponent as follows

aᵐ ⁺ ⁿ = aᵐ ⁺ ⁿ

Applying it here we get

=> ( 2² )ˣ = 2⁵

We have a law of exponent

( aᵐ )ⁿ = aᵐⁿ

Applying it here we get

=> 2²ˣ = 2⁵

Bases on both sides are equal so comparing of exponent from both sides we get

=> 2x = 5

=> x = 5 / 2

Answer 2

Answer:

We can easily find the value of x by solving the equation which is given in the question as:-)

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

Comparing powers of both side:-)

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

So,

for x = 5/2.

given equation is eligible