Question

Find x
${4}^{x} - {4}^{x - 1 } = 24$
4^(x)−4^(x−1)=24
​

Answer 1

${\large{\boxed{\colorbox{lime}{\pink{\text{Answer }}}}}}$

.

The value of X = 5/2 = 2.5

Step-by-step explanation:

${4}^{x} - {4}^{x - 1 } = 24 \\ \\ {4}^{x} - {4}^{x} \times {4}^{ - 1} = 24 \\ \\ {4}^{x} (1 - {4}^{ - 1} ) = 24 \\ \\ {4}^{x} (1 - \frac{1}{4} ) = 24 \\ \\ {4}^{x} ( \frac{4 - 1}{4} ) = 24 \\ \\ {4}^{x} \times \frac{3}{4} = 24 \\ \\ {4}^{x} = 24 \times \frac{4}{3} \\ \\ { ({2}^{2} )}^{x} = \frac{96}{3} \\ \\ {2}^{2x} = 32 \\ \\ {2}^{2x} = {2}^{5} \\ \\ 2x = 5 \\ \\ x = \frac{5}{2} = 2.5 \\ \\ used \: identity \\ \\ if \: \: \: {a}^{m} = {a}^{n} \: \: \: \: then \: \: \: m = n$

.

.

$\huge\boxed{\fcolorbox{black}{pink}{Hope.It's.Help.You!}}$

Answer 2

❥︎ Question :-

$\bf \:Find \: x : {4}^{x} - {4}^{(x - 1)} =24$

$\bf\large \underbrace\red{Answer:}$

❥︎ Identity used :- (Laws of exponents)

$\bf \: {x}^{m} \times {x}^{n} = {x}^{m + n}$

$\bf \: {x}^{m} \div {x}^{n} = {x}^{m - n}$

$\bf \:if \: {x}^{m} = {x}^{n} \implies \:m = n$

$\bf \: {x}^{ - y} = \dfrac{1}{ {x}^{y} }$

❥︎ Solution :-

$\bf \: {4}^{x} - {4}^{(x - 1)} =24$

$\bf\implies \: {4}^{x} - {4}^{x} \times {4}^{ - 1} = 24$

$\bf\implies \: {4}^{x} (1 - {4}^{ - 1} ) = 24$

$\bf\implies \: {4}^{x} (1 - \dfrac{1}{4} ) = 24$

$\bf\implies \: {4}^{x} \times \dfrac{3}{4} = 24$

$\bf\implies \: {4}^{x} = 24 \times \dfrac{4}{3}$

$\bf\implies \: {4}^{x} = 32$

$\bf\implies \: {2}^{2x} = {2}^{5}$

$\bf\implies \:2x = 5$

$\bf\implies \:x = \dfrac{5}{2}$

__________________________________________