If the following three curves intersect at one point, what is
First we find the point at which and intersect. Changing the base of the second equation gives
Then setting gives
which implies since a logarithm function is defined over positive numbers. For the value of is implying that the first two curves intersect at the point
Now, for the third curve to pass through it must be true that
which implies Therefore, our answer is The graphs of the three functions would look like the figure below.
The curve is below the curve for What is
Since the logarithm of 1 always equals zero regardless of the base, we have
so we know that the two curves meet at the point For any we know that
For any we know that
Therefore, the graphs of the two curves would look like the figure below:
Since is below for our answer is
Which of the following is not correct about the curve
The lowest value of on the curve is
The curve overlaps by a parallel translation.
The domain of the function is
The function is an increasing function.
Since the range of the function is this is not true.
Since the parallel translation of by in the positive direction of the -axis and by in the positive direction of the -axis is this is true.
Since a logarithm function is defined over positive numbers, it must be true that or
increases as increases, and so does
Therefore, our answer is