Question

8 power 12 multiply 64 power a multiply 40 power 24 multiply 25 power 13 equal to 40 power 5 find q

Answer 1

Answer:

q = 7

Step-by-step explanation:

[ We write q = p for a good calculation viewing. ]

Given,

8¹² * 64ᵖ * 40²⁴ * 25¹³ = 40⁵⁰

or, (2³)¹² * (2⁶)ᵖ * (2³ * 5)²⁴ * (5²)¹³ = (2³ * 5)⁵⁰

or, 2³⁶ * 2⁶ᵖ * 2⁷² * 5²⁴ * 5²⁶ = 2¹⁵⁰ * 5⁵⁰

or, 2³⁶⁺⁶ᵖ⁺⁷² * 5²⁴⁺²⁶ = 2¹⁵⁰ * 5⁵⁰

or, 2⁶ᵖ⁺¹⁰⁸ * 5⁵⁰ = 2¹⁵⁰ * 5⁵⁰

or, 2⁶ᵖ⁺¹⁰⁸ = 2¹⁵⁰ * 5⁵⁰ * 5⁻⁵⁰

or, 2⁶ᵖ⁺¹⁰⁸ = 2¹⁵⁰ * 5⁵⁰⁻⁵⁰

or, 2⁶ᵖ⁺¹⁰⁸ = 2¹⁵⁰ * 5⁰

or, 2⁶ᵖ⁺¹⁰⁸ = 2¹⁵⁰ [ ∵ 5⁰ = 1 ]

Comparing the powers of 2 from both sides, we get

6p + 108 = 150

or, 6p = 150 - 108

or, 6p = 42

or, p = 7

∴ q = 7