Question

Use log 2=a, log 3=b to evaluate log 216

Answer 1

answer = 3(a +b)

Explanation:

`log(2) = a \: log(3) = b \: \: \\ log(216) = log(2 * 2 * 2 * 3 * 3 * 3) \\ = log( {2}^(3) * {3}^(3) ) \\ = log(2^(3) ) + log( {3}^(3) ) \\ = 3 log(2) + 3 log(3) \\ = 3(a) + 3(b) \\ = 3(a + b) \\ \\ log(216) = 3(a + b)`