Question

How are exponential and logarithmic functions different?

Answer 1

A logarithmic function could be written as an exponential function and visa versa. For example, the exponential equation 4^3 = 64, could be written in terms of a logarithmic equation: log_4(64) = 3.

Logarithmic functions are the inverse of exponential functions...So if (4, 16) is a point on the graph of an exponential function, then (16, 4) would be the corresponding point on the graph of the inverse logarithmic function.

Answer 2

@sveta1234

Answer 3

this talks more about how they are alike

Answer 4

hmm ok brb

Answer 5

ok sorry, i hope this is what you were looking for if not just tell me.

Answer 6

Exponential Growth

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We saw an example of an exponential growth graph (showing how invested money grows over time) at the beginning of the chapter.

The exponential curve is especially important in mathematics. Exponential growth and decay are common events in science and engineering and it is valuable if you know and recognise the shape of these curves.

Example 1

Sketch the graph of y=10
​x
​​ .

Answer

Exponential Decay

graph of exponential decay
100 g of radioactive material decays
to about 12 g after 20 minutes.
Radioactive decay is the most common example of exponential decay. Here we have 100 g of radioactive material decaying over time.

Notice that the function value (the y-values) get smaller and smaller as x gets larger (but the curve never cuts through the x-axis.). Also notice that the slope of the curve is always negative, but gets closer to 0 as x increases.

Since the amount of radioactive material becomes less over time, and the amount we are talking about becomes meaningless, we normally talk about the half life, that is, the amount of time it takes for the substance to reduce to half of its original mass. In our example, it takes about 6.5 minutes for the 100 g of stuff to to decay to 50 g.

You can see another application of exponential decay in the differential equations section Application: Series RC Circuit. As the capacitor becomes fully charged, the current drops to zero. (Don't be scared by the complicated-looking mathematics in that section...)

Graph of the Logarithmic Function

Example 2

Sketch the graph of y=log
​10
​​ x.

Answer

Exponential Functions and Logarithmic Functions are Inverses

calculator button for logx 10x
NOTE: The two functions f(x)=10
​x
​​ and f(x)=log x are on the same button on your calculator because they are inverses of each other (like ex and ln x also.)

If we plot them on the same axes, we see that they are just reflections of each other in the line y = x.

In this graph, f(x)=10
​x
​​ is in green and f(x)=log x is in blue, and we can see that they are reflections of each other in y = x (plotted in red).

Answer 7

not really