log 2 =  x, log 3 = y, then log 6 is

SOLUTION

Concept:

Properties of Logarithms:

1. \({\log _a}a = 1\)
2. \({\log _a}\left( {x.y} \right) = {\log _a}x + {\log _a}y\)
3. \({\log _a}\left( {\frac{x}{y}} \right) = {\log _a}x - {\log _a}y\)
4. \({\log _a}\left( {\frac{1}{x}} \right) = - {\log _a}x\)
5. \({\rm{lo}}{{\rm{g}}_a}{x^p} = p{\rm{lo}}{{\rm{g}}_a}x\)
6. \(lo{g_a}\left( x \right) = \frac{{lo{g_b}\left( x \right)}}{{lo{g_b}\left( a \right)}}\)

Calculation:

Given:

log 2 =  x, log 3 = y

log 6 = log (2 x 3)

From 2nd property of logarithms

log 6 = log 2 + log 3

log 6 = x + y