Question 99359
Given:
.
{{{log(6,36)}}}
.
To evaluate this, let's say that it equals y. So we write the problem as:
.
{{{log(6,36) = y}}}
.
In your head, you can change this to exponential form by raising the base 6 to the y power and
setting it equal to 36. In equation form this is:
.
{{{6^y = 36}}}
.
But you can recognize that 36 is equal to {{{6^2}}}. So substitute this for 36 and the equation
becomes:
.
{{{6^y = 6^2}}}
.
Now notice that on both sides of this equation the base number is 6 and it is raised to
a power. Since the power is 2 on one side and y on the other side, the value of y has to
be 2 if both sides are equal. Therefore, you have found that y must be equal to 2. 
.
Next recall that way back at the beginning we said that:
.
{{{log(6,36) = y}}}
.
So you can substitute 2 for y and get the answer:
.
{{{log(6,36) = 2}}} 
.
Hope this helps you to see how you can do the problem without using a calculator. 
(Most calculators don't work for logarithm bases other than 10 or e anyhow unless you
use a formula known as the "change of base formula.")
.
The technique for changing from logarithmic form to exponential form is very useful in
solving many logarithmic problems. You should become proficient in using it.
.