if it is possible please bring me some example for it
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Answers (3)
One reason to work with logarithms of numbers is to convert multiplication of numbers into addition of numbers. For example, logs of power multiplication factors are converted into adding and subtracting Decibels (dB) instead. Later, you can take the anti-log to get back to regular power (watts) numbers.
Reference: engineeringtoolbox.com/decibel-d_3...
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?"
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