Help with logarithms and graphs

• shinto1
In summary: That is what I did in the first graph, by first plotting the points on ordinary graph paper, and then looking at the same points on log-log paper.In summary, the equations for each of the given cases are: 1. y = 1.333x + 0.35 on a rectilinear graph (linear format)2. y = 2x - 4 on a log-log graph (linear format)3. y = 0.5x + 1 on a semi-log graph (linear format)
shinto1
1. Determine the equation y=f(x) for each of the following cases in simplest form. All of the plots are straight lines and all coordinates are indicated with abscissa first, ordinate second (x,y).

-log y versus log x on a rectilinear graph passes through (5,7) and (2,3)

-(y-2)^2 versus x on a log-log graph passes through (1,2) and (3,4)

-√y versus x on a semi-log graph passes through (3,2) and (6,4)

2. Homework Equations

-Power Equation : y = bx^m

-Linear Equation: y = mx +b

-Exponential Equation: y = be^mx or y = b10^mx (e is base 10)

-Point slope formula: y-y1 = m(x-x1)

3. For the first problem, I found the slope, m, which is 4/3 (or 1.333) and then I used the point slope formula to get y = 1.333x + 0.35. This equation is in a linear format but the thing that confuses me is the "log y versus log x". I used this same process for the other problems but I'm still confused by the "(y-2)^2 versus x on a log-log graph" and
√y versus x on a semi-log graph". I really don't understand how to implement that part of the question into the solution, so any help would be appreciated.

Hint:

On a non-log graph, the coordinates are (10000,10000000) and (100,1000).

Hi shinto1. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

shinto1 said:
-log y versus log x on a rectilinear graph passes through (5,7) and (2,3)
I took that to be a minus sign ("–") in front of your log function, and didn't realize it wasn't until I got to the -√y plotted on semi-log paper!

[PLAIN]https://www.physicsforums.com/Nexus/statusicon/user_online.png (y-2)^2 versus x on a log-log graph passes through (1,2) and (3,4)

[PLAIN]https://www.physicsforums.com/Nexus/statusicon/user_online.png √y versus x on a semi-log graph passes through (3,2) and (6,4)

Do you understand what LawrenceC wrote about the first graph?

If a log-log plot is a straight line, then those same points plotted on an ordinary graph (rectilinear) will likewise be a straight line, but much expanded.

Last edited by a moderator:

1. What is a logarithm?

A logarithm is a mathematical function that represents the inverse of an exponential function. In simpler terms, it is used to find the power to which a base number must be raised to produce a given number.

2. How do I solve logarithmic equations?

To solve a logarithmic equation, you need to isolate the logarithm on one side of the equation and the constant on the other side. Then, use the properties of logarithms to simplify the equation and solve for the variable.

3. What is the purpose of using logarithms in graphing?

Logarithms are commonly used in graphing to transform an exponential relationship into a linear relationship. This makes it easier to analyze and understand the data, especially when the values are large or small.

4. How do I graph logarithmic functions?

To graph a logarithmic function, you need to plot a few key points and then connect them with a smooth curve. These key points can be found by substituting different values for the variable into the function and solving for the corresponding y-values.

5. What are the common properties of logarithmic functions?

The common properties of logarithmic functions include the power property, product property, quotient property, and change of base property. These properties can be used to manipulate and simplify logarithmic expressions and equations.

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