SOLUTION: Find (f o g)(16) if f(x)=3^x and f(x)=log4(x) I got this far g(16)=log4(16)=4 Please help.Thanks

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find (f o g)(16) if f(x)=3^x and f(x)=log4(x) I got this far g(16)=log4(16)=4 Please help.Thanks      Log On


   

Question 139562This question is from textbook College Algrbra
: Find (f o g)(16) if f(x)=3^x and f(x)=log4(x)
I got this far
g(16)=log4(16)=4
Please help.Thanks This question is from textbook College Algrbra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember (f o g)(x) is the same as f(g(x))


So (f o g)(16)=f(g(16))


So g%2816%29=log%284%2C%2816%29%29=2 (note: log%284%2C%2816%29%29 asks: "4 raised to what power gives me 16?". Since 4%5E2=16, this means log%284%2C%2816%29%29=2 )


So g(16)=2

Now this means that f(g(16))=f(2)

f%282%29=3%5E2=9


So f(g(16))=9