SOLUTION: f(x) = 1/3 log_3(1/4) + log_3(x) Write down D_f, the domain of f and then the solve the equation f(x) = -log_1/3(cbrt x).

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: f(x) = 1/3 log_3(1/4) + log_3(x) Write down D_f, the domain of f and then the solve the equation f(x) = -log_1/3(cbrt x).      Log On


   

Question 1159200: f(x) = 1/3 log_3(1/4) + log_3(x)
Write down D_f, the domain of f and then the solve the equation f(x) = -log_1/3(cbrt x).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
assuming given log base 3

f%28x%29+=+%281%2F3+%29log%283%2C%281%2F4%29%29+%2B+log%283%2C%28x%29%29
........log%283%2C%281%29%29=0
f%28x%29+=+%281%2F3%29%28-log%283%2C%284%29%29%29+%2B+log%283%2C%28x%29%29

f%28x%29+=+-%281%2F3+%29log%283%2C%284%29%29+%2B+log%283%2C%28x%29%29

f%28x%29+=++log%283%2C%28x%29%29-%281%2F3+%29log%283%2C%284%29%29+.......change to base 10



f%28x%29+=+log%28%28x%29%29%2Flog%28%283%29%29-log%28%284%29%29%2F3log%28%283%29%29

f%28x%29+=+log%28%28x%29%29%2Flog%28%283%29%29-%282log%282%29%29%2F%283log%283%29%29

domain:
{ x element R : x%3E0 } (all positive real numbers)
(assuming a function from reals to reals)