Question

Find the value of x.

Answer 1

HELLO DEAR,



4ˣ - 4⁽ˣ⁻¹⁾ = 24

4ˣ - 4ˣ * 1/4 = 24

4ˣ(1 - 1/4) = 24

4ˣ(3/4) = 24

4ˣ (3) = 96

4ˣ(3) = 3(32)

2²ˣ = 2⁵

2x = 5

Hence, x = 5/2



I HOPE ITS HELP YOU DEAR,
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Answer 2

HELLO DEAR ,

GOOD MORNING,

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We have :-

${4}^{x} - {4}^{x - 1} = 24 \: \: . \: \: so \\ = > {4}^{x} - \frac{ {4}^{x} }{4} = 24 \: \: \: \: \: (we \: know \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}) \\ \\ = > {4}^{x} (1 - \frac{1}{4} ) = 24 \\ \\ = > {4}^{x} ( \frac{3}{4} ) = 24 \\ \\ = > {4}^{x} = 24 \times \frac{4}{3} \\ \\ = > {4}^{x} = 32 \\ \\ => { {(2}^{2} )}^{x} = {2}^{5}$

$= > {2}^{2x} = {2}^{5} \: \: \: \: (we \: know \: ( { {a}^{m}) }^{n} = {a}^{m \times n} ) \\ \\ then \: . \\ \\ 2x = 5 \\ \\ = > x = \frac{5}{2} \: \: \: \: \: \: \: \: ( Ans )$

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Hope this will help u !!

Have a wonderful day ahead :))

# Nikky