Question

if 2 power x-1 = 3power y and 4 power x = 3 power y+1 then find the value of x and y​

Answer 1

x = (log3 - log2)/log2 &  y = b = (log 3 - log 4)/log 3

Step-by-step explanation:

x = a   &  y = b

2ᵃ⁻¹  = 3ᵇ  

=> 2ᵃ/2  = 3ᵇ

=> 3ᵇ = 2ᵃ/2

4ᵃ  = 3ᵇ⁺¹

=> (2 *2)ᵃ = 3ᵇ * 3

=>  2ᵃ * 2ᵃ = 3  * 3ᵇ

Putting 3ᵇ = 2ᵃ/2

=> 2ᵃ * 2ᵃ = 3  * 2ᵃ/2

=> 2ᵃ = 3/2

Taking log both sides

a *  log2  = log(3/2)

=> a =  log(3/2) /  log2

=> a = (log3 - log2)/log2

x = a = (log3 - log2)/log2

2ᵃ * 2ᵃ = 3  * 3ᵇ

2ᵃ = 2 * 3ᵇ

=>  2 * 3ᵇ  *  2 * 3ᵇ  = 3  * 3ᵇ

=> 3ᵇ  = 3/4

Taking log both sides

=>  b  = (log 3 - log 4)/log 3

=> y = b = (log 3 - log 4)/log 3

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