Question

If 4* - 4*-1 = 24 find the value of x
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Answer 1

Correct question:

If $\sf 4^{x}-4^{x-1} = 24$, find the value of x.

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Solution:

• $\sf 4^{x}$ can be written as $\sf 2^{2x}$
• $\sf 4^{x-1}$ can be written as $\sf 2^{2x-2}$

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$\sf 2^{2x} - 2^{2x-2} = 24$

$\sf 2^{2x} - 2^{2x} \times 2^{-2}= 24$

☆ Take $\sf 2^{2x}$ as common:

$\sf 2^{2x} (1-2^{-2} )= 24$

$\sf 2^{2x} (1- \dfrac {1}{4})= 24$

$\sf 2^{2x} (\dfrac {4-1}{4})= 24$

$\sf 2^{2x} (\dfrac {3}{4})= 24$

$\sf 2^{2x} = 24 \div \dfrac {3}{4}$

$\sf 2^{2x} = 24 \times \dfrac {4}{3}$

$\sf 2^{2x} = 8 \times 4$

$\sf 2^{2x} = 2^{3} \times 2^{2}$

$\sf 2^{2x} = 2^{3+2}$

$\sf 2^{2x} = 2^{5}$

☆ On equating powers of 2:

2x = 5

$\boxed {\bf {\red {x = \dfrac {5}{2}}}}$

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Value of x:

Value of x is $\underline {\sf {\purple {\dfrac {5}{2}}}}$