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If log a (base b) = 4 , log b (base c) = 3 and a = 32c^2, find a,b,c.
Solution
log a (base b) = 4
b^4 = a ....... Eqn *
log b (base c) = 3
c^3 = b ........eqn **
a = 32c^2
From eqn *
b^4 = a, where a =32c^2
b^4 = 32c^2 ....... Eqn 1
Fron eqn **, b= c^3
Subt. This into eqn 1 above,
(C^3)^4 =32c^2
C^12/c^2 = 32
C^10 = 32
C = (2^1/2) = root 2
Put root for c in a= 32c^2
a = 32 *2 = 64
Put 64 for a in eqn *
b^4 = a
b^4 = 64
b = root 8.
Therefore, a = 64, b= root 8 and c = root 2