Featured Answer

Asked on

Is there any body knows about logarithm? Please explain me a little about it?

if it is possible please bring me some example for it

Answers (3)

aa10331789 profile image
d0fbc544b616 profile image

A logarithmic function is the inverse of an exponential function.

For example, 5^2=25 is exponential (5 squared is 25).

The logarithmic equivalent would be log[5]25=2 (log base 5, 25 is 2).

I usually figured them out in class by reading a log as "5 to the what power equals 25?"

ctibzhueaa profile image

Logarithms are very handy things. Im sure uve seen something like 10^5 = 10000. Well what if that was 10^x = 10000. To solve for x, we can use logarithms. A logarithm is basically the opposite of an exponent. We can rewrite the equation as log10(10000) = x where 10 is a subscript. This is pronounced log base 10 10000. What i really just did was take the log base 10 of both sides

log10(10^x) = log10(10000)

remember that i said that logs were the opposite of opposites. Just as 14*x/14 = x, because dividing is the opposite of multiplying, log(10^x) = x. The other side of the equation remains log10(10000). If you plug that into a calculator( usually base 10 is just the "log" function) youll get 5.

Unfortunately not everything in life is that easy. Say you get something like 2^x = 32. Now we have to take the log2 of both sides, so x = log2(32). your calculator wont have a log2 button, so well have to convert log10 to log2. To do this we use the change of base formula.

log10(n)/log10(b) = logb(n) where n is the number inside the log and b is the base. Infact log10 doesnt even have to be used, but you have a button for it so well use that.

so going back to our original equation.

x = log2(32)

x = log10(32)/log10(2)

x = 5

Now, in higher math, youll come across a mathmatical constant named e. e is extremely handy, and therefore in higher math we tend only to use loge, also known as ln, the natural logarithm. In exponential functions, e is the natural rate of change, im not going to go into that but basically if you have the equation y = e^x, the slope of the graph at x will = x.

anyway one last example using e

e^(5x+2) = 20

ln(e^(5x+2)) = ln(20)

5x + 2 = ln(20)

5x = ln(20)-2

x = (ln(20)-2)/5

x = well i dont have a calculator on me so you can work it out