SOLUTION: Given loga(2) = 0.3 and loga (3) = 0.48. Find: 1. loga (12) 2. loga (1/18) 3. loga (\sqrt[3]{9})

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given loga(2) = 0.3 and loga (3) = 0.48. Find: 1. loga (12) 2. loga (1/18) 3. loga (\sqrt[3]{9})      Log On


   

Question 1089582: Given loga(2) = 0.3 and loga (3) = 0.48. Find:
1. loga (12)
2. loga (1/18)
3. loga (\sqrt[3]{9})
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:log%282%29+=+0.3 and log%283%29+=+0.48 (I guess all is in base 10)
Find:
1.
log%2812%29
=log%282%5E2%2A3%29
=log%282%5E2%29%2Blog%283%29
=2log%282%29%2Blog%283%29
=2%2A0.3%2B0.48
=0.6%2B0.48
=1.08
2.
log%281%2F18%29
=log%281%2F%282%2A3%2A3%29%29
=log%281%29-log%282%2A3%2A3%29
=0-%28log%282%29%2Blog%283%29%2Blog%283%29%29
=-%280.3%2B0.48%2B0.48%29
=-1.26

3. loga (\sqrt[3]{9})-> if this is log%28sqrt%283%29%2F9%29, you will have
log%28sqrt%283%29%2F9%29
=log%28sqrt%283%29%29-log%289%29
=log%283%5E%281%2F2%29%29-log%283%5E2%29
=%281%2F2%29log%283%29-2log%283%29
=%281%2F2-2%29log%283%29
=-%283%2F2%29log%283%29
=-%283%2F2%29%2A0.48
=-%281.44%2F2%29
=-0.72