Question

Given: logx/logy= 3/2 and log (xy) = 5 ; find the values of x and y.
Solve: log5(x+1) - 1 = 1 + log5(x-1)

Answer 1

logx/logy = 3/2 

⇒ log y = (2log x )/3  ........... i

log(xy) = 5

⇒log x + log y = 5           ...... ii

let log x = a


using i we get 

a + 2a/3 = 5

⇒ 3a + 2a = 15

⇒ a = 3

so log x = 3 ⇒ x = 10³ 

so x = 1000 ANSWER

so log y = 2log x/ 3 

⇒ log y = 2 

y = 10² = 100 ANSWER





log₅(x+1) - 1 = 1 + log₅(x-1)

⇒ log₅(x+1)  - log₅(x-1) = 2

⇒ $log_5[\frac{x+1}{x-1}]$ = $log_55^2$

cancelling the log from both sides

⇒ x+1 = 25x - 25

⇒24x = 26

⇒ x = $\frac{13}{12}$ ANSWER

Answer 2

Answer:logx/logy = 3/2 

⇒ log y = (2log x )/3  ........... i

log(xy) = 5

⇒log x + log y = 5           ...... ii

let log x = a

using i we get 

a + 2a/3 = 5

⇒ 3a + 2a = 15

⇒ a = 3

so log x = 3 ⇒ x = 10³ 

so x = 1000 ANSWER

so log y = 2log x/ 3 

⇒ log y = 2 

y = 10² = 100 ANSWER

Step-by-step explanation: