Quick Answer: How Does A Logarithmic Scale Work?

What does a logarithmic scale mean?

From Wikipedia, the free encyclopedia.

A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers..

How are exponential and logarithmic functions used in real life?

Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).

What is the relationship between exponential or logarithmic equations?

Logarithms are the “opposite” of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs “undo” exponentials. Technically speaking, logs are the inverses of exponentials. On the left-hand side above is the exponential statement “y = bx”.

What is the difference between a linear and logarithmic scale?

Linear graphs are scaled so that equal vertical distances represent the same absolute-dollar-value change. The logarithmic scale reveals percentage changes. … A change from 100 to 200, for example, is presented in the same way as a change from 1,000 to 2,000.

What does a straight line on a logarithmic scale mean?

A plot of the logarithm of the freefall distance as a function of the logarithm of time yields a straight line of slope 2. The slope of a log-log plot gives the power of the relationship, and a straight line is an indication that a definite power relationship exists.

What is the meaning of logarithmic?

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

What is the difference between linear and exponential?

Exponential Functions. In linear functions, rate of change is constant: as x goes up, y will go up a consistent amount. In exponential functions, the rate of change increases by a consistent multiplier—it will never be the same, but there will be a pattern.

What does a logarithmic graph tell you?

Same data, different perspectives But the logarithmic graph shows a flattening of the line much earlier because of the way the scale has been compressed. It also makes it possible to fit a large or widespread set of results onto a graph that might otherwise not fit in a linear way.

What is the difference between exponential and logarithmic graphs?

The logarithmic function is the inverse function of the exponential function. This is means that if a^x = b (exponential), then log base a (b) = x. (logarithmic). Therefore, exponential and logarithmic functions are not the same.

How do you read a logarithmic scale graph?

By using the top plot, [H+] can be read directly from the X-axis; for example, at 45% saturation, [H+] = 1.0 x 10-5. By using this bottom plot, [H+] must be calculated by taking the antilog of the negative value of the log value read from the X-axis; for example, at 45% saturation, [H+] = antilog (-5.0) = 10-5.

What does a logarithmic curve look like?

The logarithmic function may look like the graph below. The negative in front of the function reflects the function over the x-axis, but all other properties of the logarithmic function hold. Here, as a decreases, the magnitude of a increases. As this happens, the graph decreases at a quicker rate as x increases.

Is pH a log?

The pH scale is logarithmic, essentially meaning the difference in 1 pH unit is a difference of 10 times! Last week we introduced exactly what we are measuring when we take a pH measurement – hydrogen ion activity.

Why would you use a logarithmic scale?

There are two main reasons to use logarithmic scales in charts and graphs. The first is to respond to skewness towards large values; i.e., cases in which one or a few points are much larger than the bulk of the data. … The equation y = log b (x) means that y is the power or exponent that b is raised to in order to get x.

Is logarithmic the same as exponential?

Logarithmic growth is the inverse of exponential growth and is very slow. … This terminological confusion between logarithmic growth and exponential growth may be explained by the fact that exponential growth curves may be straightened by plotting them using a logarithmic scale for the growth axis.

Is ex logarithmic or exponential?

You can see straight away that the logarithm function is a reflection of the exponential function in the line represented by f(x) = x. In other words, the axes have been swapped: x becomes f(x), and f(x) becomes x. The exponential function f(x) = ex is the inverse of the logarithm function f(x) = ln x.

What does exponential growth look like on a logarithmic graph?

If you show exponential growth on an exponential scale – meaning, our log scale –, the exponential effect evens out. We get a straight line. That means: If you see a straight line in a log-scaled chart, something grows exponentially. Every minute/day/year, the amount of something will double (or halve).