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
.
It is obvious that the radicals with negative sign tends to be less than those that are positive. So from there you already know a basic order. Now to be sure, you can use a calculator or just solve by squaring the whole number to find the radical form.
6 1/8 - (3 3/8 + 2 1/8) =
6 1/8 - (5 4/8) =
5 9/8 - 5 4/8 =
5/8 yds <===