SOLUTION: Evaluate log6 (36) without using your calculator.

Question 99359: Evaluate log6 (36) without using your calculator.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To evaluate this, let's say that it equals y. So we write the problem as:
.

.
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:
.

.
But you can recognize that 36 is equal to . So substitute this for 36 and the equation
becomes:
.

.
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:
.

.
So you can substitute 2 for y and get the answer:
.

.
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.
.

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