SOLUTION: Given f(x)=3log6(2x-1) find f(5)to the nearest hundredth.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Given f(x)=3log6(2x-1) find f(5)to the nearest hundredth.      Log On


   

Question 276285: Given f(x)=3log6(2x-1) find f(5)to the nearest hundredth.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=3log%286%2C+%282x-1%29%29
f%285%29=3log%286%2C+%282%285%29-1%29%29
f%285%29=3log%286%2C+%2810-1%29%29
f%285%29=3log%286%2C+%289%29%29
Now what do we do? How do we find a base 6 logarithm? No calculators I know can do base 6 logarithms. What we need to change the base to one our calculators "know:. Fortunately there is a change of base formula for logarithms: log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29. Using this to change our base 6 log into an expression of base 10 logs we get:
f%285%29=3%28log%28%289%29%29%2Flog%28%286%29%29%29
Now we can go to our calculators and find the two base 10 logarithms, divide them and then multiply by 3. (I'll leave that up to you to do.)

P.S. Many calculators also can do base e (ln) logarithms. If we used them instead of base 10 our equation would become:
f%285%29=3%28ln%289%29%2Fln%286%29%29
Believe it or not, this gives the same answer! (Try it if you don't believe it.)