Intersection point of y=logx and y=1/2log(x+1)

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 .

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