What is the meaning of the base of the function #y=-log(x)#?

1 Answer
Jul 11, 2018

I tried this:

Explanation:

The base #b# helps you to evaluate the log for values of #x# giving you the corresponding value of #y#.

Let us consider an example:

#log_color(red)(2)(x)#

where the base is #2#.
We can find this log for various values of #x# considering the definition of log:

#log_2(x)=c#
so that: #x=2^c#

if #x=4# then we get:
#log_2(4)=?#
we see that has to be:
#log_2(4)=2#
because: #2^2=4#

if #x=8# then we get:
#log_2(8)=?#
we see that has to be:
#log_2(4)=3#
because: #2^3=8#

Now let us consider your function with base #2#:

#color(red)(y=-log_(2)(x))#

we can build a table of values:
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