Question

If 5^a = 8^b = 10^c, then the value of c is

Answer 1

Answer:

let 5^a=8^b=10^c=k

so 5^a=k

5=k^1/a

similarly 8=k^1/b or 2=k^1/3b

and 10=k^1/c

now 5×2=10

(k^1/a)(k^1/3b)=k^1/c

So 1/a+1/3b=1/c

c=(3ab/3b+a)