Math, asked by sarah8521, 5 months ago

53. Given that log 3 to the base p = x and log 5 to the base p = y, find the logarithm of the following base p:
i)5/3

ii)75

iii) 5p²/27

answers according to book:
i)y-x

ii)2y+x

iii)y-3x+2

how to solve this, please show me the method

Answers

Answered by sulochanakushumalia
0

Answer:

Solution: Given, log(base5) (x + y) + log(base5) (x − y) = 3

Or log(base5) (x + y)*(x-y) =3

Or x^2 –y^2 = 5^3 = 125————-1)

log(base2) y − log(base2) x = 1 − log(base2) 3= log(base2) 2 – log(base2) 3

log(base2) y/x = log(base2) 2/3

y/x = 2/3

y = 2x/3

from eq 1) x^2 – (2x/3)^2 = 125

x^2 – (4x^2/9) = 125

5x^2 = 125*9 or x^2 = 225

x = 15

y= 2x/3 = 30/3 = 10

xy = 15*10 =150

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