Hello
The minimum of the function is ?
What's the process to solve this problem?
Thanks.
the process is the same as for all problems of this type, find it's derivative and set it equal to zero. if necessary, use the second derivative to verify which of the critical points is a minimum
you will need the change of base formula to change all the logs to ln though
Change of Base Formula for Logarithms:
or maybe noticing that will simplify the problem a bit. but i'd go with my first suggestion
Hello, Patrick_John!
I will assume that we are not allowed to use Calculus . . .
The logs have two different bases; we'll make them the same.Find the minimum of the function: .
Let
. . Then: .
. . Take logs (base 2): .
. . Then: .
. . Hence: .
Substitute into the original equation: .
Let
Then we have: .
This is an up-opening parabola; its minimum is at its vertex.
The vertex formula is: .
We have: .
Hence, the vertex is at: .
Therefore, the minimum is: .