Question

5^x+1 - 5^x-1 =24 find the value of x with full explanation ​

Answer 1

Answer:-

Given:-

5ˣ⁺¹ - 5ˣ⁻¹ = 24

Using aᵐ⁺ⁿ = aᵐ × aⁿ and aᵐ⁻ⁿ = aᵐ / aⁿ in LHS we get,

⟹ 5ˣ × 5¹ - 5ˣ/5¹ = 24

Let 5ˣ = a.

⟹ a × 5 - a/5 = 24

⟹ 5a - a/5 = 24

⟹ (25a - a)/5 = 24

⟹ 24a/5 = 24

⟹ a = 24 × 5/24

⟹ a = 5

Therefore,

⟹ 5ˣ = 5

5 can be written as 5¹.

⟹ 5ˣ = 5¹

Here, bases are equal both sides, so their powers are also equal.

⟹ x = 1

∴ Required answer is 1.

Answer 2

Step-by-step explanation:

ANSWER ✍️

_____________

Given:-

5ˣ⁺¹ - 5ˣ⁻¹ = 24

Using aᵐ⁺ⁿ = aᵐ × aⁿ and aᵐ⁻ⁿ = aᵐ / aⁿ in LHS we get,

• ⟹ 5ˣ × 5¹ - 5ˣ/5¹ = 24

• Let 5ˣ = a.

• ⟹ a × 5 - a/5 = 24

• ⟹ 5a - a/5 = 24

• ⟹ (25a - a)/5 = 24

• ⟹ 24a/5 = 24

• ⟹ a = 24 × 5/24

• ⟹ a = 5

SO,

-----> 5ˣ = 5

5 can be written as 5¹.

-----> 5ˣ = 5¹

Here, bases are equal both sides, so their powers are also equal.

----->x = 1

hope this helps you