Question

$5 ^{6x} = 125 ^{2}$
Then find the value of x.​

Answer 1

$5 {}^{6x} = 125 {}^{2} \\ = 5 {}^{6x} = (5 {}^{3} ) {}^{2} \\ = 5 {}^{6x} = 5 {}^{6}$

as the bases are equal their exponents are also equal

there fore

$6x = 6 \\ = x = 6 \div 6 \\ = x = 1$

Answer 2

Answer:

• The value of x = 1

Step-by-step explanation:

Given that:

• 5⁶ˣ = 125²

To Find:

• The value of x.

Finding the value of x:

⇒ 5⁶ˣ = 125²

⇒ (5³)²ˣ = 125²

⇒ 125²ˣ = 125²

• 125 cancelled both sides.

⇒ 2x = 2

⇒ x = 2/2

⇒ x = 1

K. Law's of Indices:

1) aˣ × aʸ = aˣ⁺ʸ

Eg: 3³ × 3² = 3³⁺² = 3⁵

2) aˣ ÷ aʸ = aˣ⁻ʸ

Eg: 3³ ÷ 3² = 3³⁻² = 31

3) (aˣ)ʸ = aˣʸ

Eg: (3²)³ = 3⁶

4) a° = 1

Eg: 3° = 1

5) ˣ√a = (a)¹/ˣ

Eg: ²√3 = 3¹/²

6) a⁻ˣ = 1/aˣ

Eg: 3⁻² = 1/3²

7) aˣ = aʸ

→ x = y

Eg: 3²ˣ = 3⁴

→ 2x = 4