Answer:
The intersection is .
The Problem:
What is the intersection point of and
?
Step-by-step explanation:
To find the intersection of and
, we will need to find when they have a common point; when their
and
are the same.
Let's start with setting the 's equal to find those
's for which the
's are the same.
By power rule:
Since implies
:
Squaring both sides to get rid of the fraction exponent:
This is a quadratic equation.
Subtract on both sides:
Comparing this to we see the following:
Let's plug them into the quadratic formula:
So we have the solutions to the quadratic equation are:
or
.
The second solution definitely gives at least one of the logarithm equation problems.
Example: has problems when
and so the second solution is a problem.
So the where the equations intersect is at
.
Let's find the -coordinate.
You may use either equation.
I choose .
The intersection is .
