Question

find the value of x:
(iii) 2 ^ 3 + 2 ^ x = 2 ^ 4​

Answer 1

Answer:

x=3

Step-by-step explanation:

2³ + 2^x = 2⁴

2^x = 2⁴ - 2³

2^x = 16 - 8

2^x = 8

As we know 2³ is 8

x = 3

Answer 2

Answer:

• The value of x satisfying the given equation is 3.

Solution:

Given Equation:-

→ 2³ + 2ˣ = 2⁴

Can be written as:-

→ 2ˣ = 2⁴ - 2³

→ 2ˣ = 2³(2¹ - 1) [Taking 2³ as common]

→ 2ˣ = 2³(2 - 1)

→ 2ˣ = 2³ × 1

→ 2ˣ = 2³

Comparing base, we get:-

→ x = 3

★ Therefore, the value of x satisfying the given equation is 3.

Learn More:

Laws of exponents.

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

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

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

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

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

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

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

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

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