Question 388101: logx is greater than or equal to log(base 4) x^2
What is x equal to?
It tells me to graph it, but i can't figure out how to....
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I presume the statement is:
log(4,x) >= log(4,x^2)
This means that the log of x to the base 4 is greater than or equal to log of x^2 to the base 4.
find x.
to find where they cross, you need to graph both equations.
we'll graph log(4,x) and log(4,x^2) to see if they cross anywhere.
from the graph, it looks like this occurs when goes from 0 to 1.
when x is negative doesn't apply because the graph of log(4,x) is only valid when x is greater than 0.
log(4,0) is not valid.
log(4,-x) is not valid.
you probably just need to graph them from x = 0 to x = 2.
The crossing point is at x = 1.
log(4,x) >= log(4,x^2) in the interval 0 < x <= 1
the graph of the log(4,x^2) is still not valid at x = 0.
the graph of the log(4,x^2) is valid when x is negative because x^2 is positive.
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