Difference Between Logarithmic and Exponential

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function y = log_ax is defined to be equivalent to the exponential equation x = a^y. ... So you see a logarithm is nothing more than an exponent.

Is logarithmic the same as exponential?
How do you tell if a graph is exponential or logarithmic?
What is the relationship between exponential or logarithmic equations?
Why would you use a logarithmic scale?
How are exponential and logarithmic functions used in real life?
What is the difference between linear and logarithmic?
What are the similarities between exponential and logarithmic functions?
How do you know if a graph is exponential?
What is the definition of exponential?
How do you convert between exponential and logarithmic form?
Why is log the inverse of exponential?

Is logarithmic the same as exponential?

Logarithmic growth is the inverse of exponential growth and is very slow. ... In microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. During this bacterial growth phase, the number of new cells appearing are proportional to the population.

How do you tell if a graph is exponential or logarithmic?

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.

What is the relationship between exponential or logarithmic equations?

The logarithmic and exponential operations are inverses. If given an exponential equation, one can take the natural logarithm to isolate the variables of interest, and vice versa. Converting from logarithmic to exponential form can make for easier equation solving.

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 second is to show percent change or multiplicative factors.

How are exponential and logarithmic functions used in real life?

Using Logarithmic Functions

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 difference between linear and logarithmic?

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 are the similarities between exponential and logarithmic functions?

The natural exponential function is y = f(x) = ex and the natural logarithmic function is f(x) = loge x = lnx , where x > 0. Also we can see that to graph and exponential function it always has to pass through the point (0,1). However, both of these functions also have similarities.

How do you know if a graph is exponential?

Graphs of Exponential Functions

The graph passes through the point (0,1)
The domain is all real numbers.
The range is y>0.
The graph is increasing.
The graph is asymptotic to the x-axis as x approaches negative infinity.
The graph increases without bound as x approaches positive infinity.
The graph is continuous.

What is the definition of exponential?

1 : of or relating to an exponent. 2 : involving a variable in an exponent 10^x is an exponential expression. 3 : expressible or approximately expressible by an exponential function especially : characterized by or being an extremely rapid increase (as in size or extent) an exponential growth rate.

How do you convert between exponential and logarithmic form?

To change from exponential form to logarithmic form, identify the base of the exponential equation and move the base to the other side of the equal sign and add the word “log”. Do not move anything but the base, the other numbers or variables will not change sides.

Why is log the inverse of exponential?

Thus, the domain of the logarithm base function is the range of the function (all positive numbers) and the range of the logarithm base function is the domain of the function (all numbers). since the logarithmic function and the exponential function are inverses of each other.