Suppose that u log 3 and v log 5 Find possible formulas fo

Suppose that u = log (3) and v = log (5). Find possible formulas for the following expressions in terms of u and/or v. Your answers should NOT involve any log\'s. a) log (0.6) = u-v b) log (0.125) = c) log (900) = d)log(squareroot3375) =

Solution

a) log (0.6) = log ( 6/10) = log (3/5) = log3 - log 5 = u - v ( as log a/b = log a - log b)

b) log ( .125) = log ( 0.5)³ = 3log( 0.5) == 3log ( 5/10) = 3( log 5 - log 10) = 3 (v -1) ( as log 10 = 1)

c) log (900) = log (30)² = 2log 30 = 2log ( 3*10) = 2( log 3 + lof 10) = 2(u + 1) ( as log a^b = b log a, log ab = log a + log b)

d) log ( 3375) = log ( 3³ * 5³ )^1/2 = 1/2 log ( 3*5)³ = 3/2 log(3*5) = 3/2( log3 + log5) = 3/2( u + v)