SOLUTION: <pre><font size = 2 color = "indigo"><b> can someone help me solve: given log<sub>b</sub>3 = 0.6826 and log<sub>b</sub>7 = 1.2091, evaluate log<sub>b</sub>21. completely lost.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: <pre><font size = 2 color = "indigo"><b> can someone help me solve: given log<sub>b</sub>3 = 0.6826 and log<sub>b</sub>7 = 1.2091, evaluate log<sub>b</sub>21. completely lost.      Log On


   

Question 108168: 

can someone help me solve: given logb3 = 0.6826 
and logb7 = 1.2091, evaluate logb21. 
completely lost.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

can someone help me solve: given logb3 = 0.6826 
and logb7 = 1.2091, evaluate logb21. 
completely lost.

You need to know this basic rule of logarithms:

logb(X·Y) = logbX + logbY

and the fact that 21 = 3·7, to get

logb(3·7) = logb3 + logb7

then since you are given that 

logb3 = 0.6826 and logb7 = 1.2091

logb(3·7) = logb3 + logb7 = 0.6826 + 1.2091 = 1.8917

Edwin