What are logs?? (1 Viewer)

[Brontecat]

What are logs??

i've just started this topic so im not too sure what exactly a log is and i dont understand how it just goes away
it would be rlly helpful if someone could give an example and explain it

 

[jet]

A log is basically the reverse of an exponent, or a power.
When you have some equations, you may end up with an equation of the form
a^x = b, where a and b are arbitrary numbers, and x is the pronumeral we need to solve for.
You can obviously see, that if b cannot be expressed as a power of a, then it is very difficult to solve. Logs help with this.
If an exponent can be written b = a^x then the log is written:
x = log_ab; where x is called the exponent, and a is called the base.
Then, we can use a set of derived 'log laws' to help us solve for x.
Using the index laws (which you would have probably learnt in year 10), such as a^{x + y} = a^x * a^y, and (a^x)^y = a^xy, we can work out that
log_a(xy) = log_ax + log_ay
log_x^y = ylog_ax
log_a(x/y) = log_ax - log_ay
Another important one is the change of base law, which states that log_ax = (log_bx)/(log_ba); where b can be any number, but we normally choose 10 or e (euler's number) as these are the logs available to us on our calculator.

Finally, you asked how logs disappear. Well, noticing that a log, and exponent of the same base are the opposite of each other they should cancel out. So:
a^log_ax = x
and log_b b^y = y log_bb = y

 

[pman]

Two definitions:
1. the invers of an exponential (draw y=e^x then mirror on y=x). Used for doing multiplication before calculators.
2. The trunk of a tree that has been cut down.

 

[Uncle]

Just remember logs turn "products" into "sums"