Question

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

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Answer 1

Given:-

${4}^{x} - {4}^{x - 1} = 24$

To Find:-

The Value of x

Solution:-

${4}^{x} - {4}^{x - 1} = 24$

$= > {4}^{x} - {4}^{x} \times {4}^{ - 1} = 24$

$=> {4}^{x}(1 - {4}^{ - 1} ) = 24$

$= > {4}^{x}(1 - \frac{1}{4}) = 24$

$=> {4}^{x}( \frac{4}{4} - \frac{1}{4}) = 24$

$= > {4}^{x}( \frac{4 - 1}{3}) = 24$

$=> {4}^{x}( \frac{3}{4}) = 24$

$= > {4}^{x} = 24 \times \frac{4}{3}$

$= > {4}^{x} = 8 \times 4$

$= > {4}^{x} = 32$

$= > {2}^{2x} = 32$

$= > {2}^{2x} = {2}^{5}$

$= > 2x = 5$

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

Answer 2

above one is correct...