Question

(ii) 4^ x- 4^x-1= 24​

Answer 1

Answer:

x=5/2

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=2^5

2^2x=2^5

2x=5

x=5/2

Answer 2

Question:

Find the value of x if ;

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

Answer:

x = 5/2

Note:

• ${a}^{x} \times {a}^{y} = {a}^{x + y}$

• $\frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y}$

• ${ ({a}^{x})}^{y} = {a}^{x \times y}$

• ${a}^{x} \times {b}^{x} = {(a \times b)}^{x}$

• $\frac{ {a}^{x} }{ {b}^{x} } = { (\frac{a}{b}) }^{x}$

• ${a}^{ - x} = \frac{1}{ {a}^{x} }$

• ${a}^{0} = 1$

• $If \: \: {a}^{x} = {a}^{y} , \: \: then \: \: x = y$

Solution:

We have ;

$= > {4}^{x} - {4}^{x - 1} = 24 \\ = > {4}^{x - 1} \times (4 - 1) = 24 \\ = > {4}^{x - 1} \times 3 = 24 \\ = > {4}^{x - 1 } = \frac{24}{3} \\ = > {4}^{x - 1} = 8 \\ = > {( {2}^{2} )}^{x - 1} = {2}^{3} \\ = > {2}^{2(x - 1)} = {2}^{3} \\ = > 2(x - 1) = 3 \\ = > x - 1 = \frac{3}{2} \\ = > x = \frac{3}{2} + 1 \\ = > x = \frac{3 + 2}{2} \\ = > x = \frac{5}{2}$

Hence,

The required value of x is 5/2 .