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 .

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

your answer would be 12