Question

Simplify: 6^(2x-1)=36^(x-1) + 1080

Answer 1

Given question is 6^(2x-1) = 36^(x-1) + 1080

Solution:
6²ˣ . 6⁻¹ = 36ˣ . 36⁻¹ + 1080

6² . 6ˣ . 1 / 6 = 36ˣ . 1/36 + 1080

36 / 6 . 6ˣ = 36ˣ / 36 + 1080

6 . 6ˣ - 36ˣ / 36 = 1080

Multiplying whole equation by 36, we get:

216 . 6ˣ - 36ˣ = 38880

Taking 6ˣ common from left hand side, we get:

6ˣ (216 - 6²) = 38880

6ˣ (216 - 36) = 38880

6ˣ (180) = 38880

6ˣ = 38880/180

6ˣ = 216

Taking logarithm to base 10 on both sides, we get:

log (6ˣ) = log 216

x . log 6 = log 216

x = log 216 / log 6

x = 2.334 / 0.778

x = 30

This is the required value of "x".
Hope this will help you. Thanks

Answer 2

6^(2x-1)=36^(x-1) + 1080

6^2x × 6-¹ = 6²^(x-1) + 1080

6^2x / 6 = 6²^(x-1) + 1080

6^2x/6= 6^2x-2 +1080

6^2x/6 = 6^2x × 6-² +1080

6^2x/6 = 6^2x /6² +1080


6^2x/6 - 6^2x / 6² = 1080

6^2x/6 - 6^2x / 36 = 1080

6^2x( 1/6- 1/36) = 1080

6^2x( (6-1)/36) = 1080

6^2x( 5/36) = 6³×5

6^2x=( 6³×5×36)/5

6^2x=( 6³×36)

6^2x=( 6³×6²)

6^2x=( 6^5)

On Comparing

2x= 5

x= 5/2

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Hope this will help you...