Question

If 2^4 x 4^3 = 4^x, then value of x is.

a) 5 (b) 7 c)4 d)-5. step by step pls​

Answer 1

Answer:

5

Mark as brainliest answer.

Step-by-step explanation:

2^4 x 4^3 = 4^x

4^2 x 4^3 = 4^x

4^5 = 4^x

x=5

Answer 2

$\textsf{\large{\underline{Solution}:}}$

Given That:

$\rm: \longmapsto {2}^{4} \times {4}^{3} = {4}^{x}$

$\rm: \longmapsto {2}^{4} \times {( {2}^{2} )}^{3} = {4}^{x}$

$\rm: \longmapsto {2}^{4} \times ( {2}^{2 \times 3} ) = {4}^{x}$

$\rm: \longmapsto {2}^{4} \times {2}^{6} = { ({2}^{2}) }^{x}$

$\rm: \longmapsto {2}^{4 + 6} = {2}^{2x}$

$\rm: \longmapsto {2}^{10} = {2}^{2x}$

Comparing base, we get:

$\rm: \longmapsto 2x = 10$

$\rm: \longmapsto x = 5$

★ So, the value of x is 5.

$\textsf{\large{\underline{Learn More}:}}$

Laws Of Exponents: If a, b are positive real numbers and m, n are rational numbers, then the following results hold.

$\rm 1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\rm 2. \: \: ({a}^{m})^{n} = {a}^{mn}$

$\rm 3. \: \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\rm4. \: \: {a}^{m} \times {b}^{m} = {(ab)}^{m}$

$\rm5. \: \: \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$\rm6. \: \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\rm7. \: \: {a}^{n} = {b}^{n} \rightarrow a = b, n \neq0$

$\rm8. \: \: {a}^{m} = {a}^{n} \rightarrow m = n, a \neq 1$