Question

Find x :-

${4}^{x} - {4}^{x - 1} = 24$
​

Answer 1

Step-by-step explanation:

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

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

4^x(3/4)=24

4^x=24(4)/3

4^x=32

Hence x=3/2

Answer 2

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

➙4ˣ - 4ˣ⁻¹=24

Taking out 4ˣ common from the Equation

➙4ˣ(1-1/4)= 24

➙4ˣ (4-1/4)= 24

➙4ˣ (3/4)= 24

shifts 3/4 to constant side

➙4ˣ = 24× 4/3

➙4ˣ = 8×4

➙4ˣ = 32

Here,32 can also be written as 2⁵

➙4ˣ = 2⁵

➙2²ˣ=2⁵

Since, 2 lies on both sides so,it gets automatically cancelled [ Reason : when bases are same on both sides of the Equation it gets cancelled]

➙2x= 5

➙x= 5/2

Check:

➙4ˣ = 32

put x = 5/2

$\bold{ \sf = > {4}^{ \frac{5}{2} }}$

$\bold{ \sf = > { ({2}^{2}) }^{ \frac{5}{2}} }$

$\bold{\sf = > {2}^{ \frac{10}{2} } = {2}^{5} = 32}$