Expert: Steve Holleran - 5/28/2008

Question
Use logarithms to solve the problems
Q1.What is the cube root? if D = V/0.5236.V = 100.
Find the value of the questions below
Q2.Find the cube root of 0.04796
Q3. 1215 (3/2)

Answer
Hi Max,

1.  Do you mean here that you want D = cu rt(V / .5236) and V = 100?

   If so, the you have log D = log [cu rt(100/.5236)]

                      log D = log[(100/.5236)^(1/3)]

                      log D = (1/3) * (log 100 - log .5236)

                      log D = (1/3) * (2 - log .5236)

                      log D = .7603

so                        D = 10^.7603 = 5.758


2.  Same thing:   x = cu rt(.04796) = (.04796)^(1/3)

            so   log x = (1/3) log (.04796)

                 log x = -0.4397   so x = 10^(-.4397) = 0.3633


3.  Do you mean 1215^(3/2)?  

   If so, then x = 1215^(3/2)  so log x = log [1215^(3/2)

   and    log x = (3/2) * log 1215 = 1.5 * 3.084 = 4.626
 
   and then x = 10^4.626 = 42,266.86


Steve