Question 318300
<pre><b>
If you know that 2 raised to the 3 power is 8 then you know a logarithm,

The fill-in-the-blank problem:

{{{log(2,(8))}}} = ___

amounts to the following fill-in-the-blank problem.

2 raised to the ___ power is 8.

In both cases the number that goes in the blank is 3.

In other words, a logarithm IS the exponent to which we must raise the
base in order get the number that we are taking the log of.

Since {{{5^2 = 25}}} that means that {{{log(5,(25)) = 2}}}

Since {{{7^1 = 7}}} that means that {{{log(7,(7)) = 1}}}

Since {{{10^8 = 100000000}}} that means that {{{log(10,(100000000)) = 8}}} 

Since {{{6^0 = 1}}} that means that {{{log(6,(1)) = 0}}}

Since {{{B^A = C}}} that means that {{{log(B,(C)) = A}}}

Since {{{5^(-1) = 1/5}}} that means that {{{log(5,(1/5)) = -1}}}

Remember

1. The base of the exponent equals the base of the log.
2. The log equals the exponent
3. The result of the exponentiating is what the log is taken of.

Edwin</pre>