Question

25^a= 27^b=225^c where a,band c are non zero real numbers then the value of c is​

Answer 1

Answer:

c = (a log5)/log15 = (3b log3)/(2 log15)

Step-by-step explanation:

Given,

25ᵃ = 27ᵇ = 225ᶜ

or, (5²)ᵃ = (3³)ᵇ = (15²)ᶜ

or, 5²ᵃ = 3³ᵇ = 15²ᶜ

Taking the first and the third term, we get

5²ᵃ = 15²ᶜ

or, 2a log5 = 2c log15 [ taking log ]

or, a log5 = c log15

or, c = (a log5)/log15 ..... (1)

Again taking the second and third term, we get

3³ᵇ = 15²ᶜ

or, 3b log3 = 2c log15 [ taking log ]

or, c = (3b log3)/(2 log15) ..... (2)

Combining the two values from (1) and (2), we get

c = (a log5)/log15 = (3b log3)/(2 log15)

Thus we obtain value of c in terms of a or b.

Note:

There must be another condition given by which we will be able to find the exact values of a, b, c in real numbers.