Question

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Answer 1

Question :

Find x, y, z if 15³ × 12² × 16⁴ = 2ˣ × 3ʸ × 5ᶻ

Solution :

15³ × 12² × 16⁴ = 2ˣ × 3ʸ × 5ᶻ

We know that,

• 15 = 3 × 5
• 12 = 3 × 2²
• 16 = 2⁴

⇒ ( 3 × 5 )³ × ( 3 × 2²)² × ( 2⁴ )⁴ = 2ˣ × 3ʸ × 5ᶻ

Using ( ab )^m = a^m × b^m

⇒ 3³ × 5³ × 3² × ( 2² )² × ( 2⁴ )⁴ = 2ˣ × 3ʸ × 5ᶻ

Using ( a^m )^n = a^mn

⇒ 3³ × 5³ × 3² × 2⁴ × 2¹⁶ = 2ˣ × 3ʸ × 5ᶻ

By Rearranging we get,

⇒ 2⁴ × 2¹⁶ × 3³ × 3² × 5³ = 2ˣ × 3ʸ × 5ᶻ

Now using a^m × a^n = a^( m + n )

⇒ 2⁽⁴ ⁺ ¹⁶⁾ × 3⁽³ ⁺ ²⁾ × 5³ = 2ˣ × 3ʸ × 5ᶻ

⇒ 2²⁰ × 3⁵ × 5³ = 2ˣ × 3ʸ × 5ᶻ

Comparing on both sides we get

• x = 20
• y = 5
• z = 3

Therefore we found the required answer.

Answer 2

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