In this video, you will learn how to solve
logarithm question using comparison method
In the first example, we have log_3 x =log_9
(5x+6)
First, make the base the same.
You can either change both to 3 or 9.
It would be easier to change to the smaller
number.
Using the law of change of base, we change
the RHS into log with base 3
The denominator can be simplified by changing
9 to 3 square and bring the power down
Then, simplify log base 3 3 to 1.
The fraction 1/2 can be changed into the power
Now, we have LHS and RHS with the same log
base 3.
By comparison, x must be equal to (5x+6)^(1/2)
Then,solve the equation and we will obtain
two answers.
We have to reject the negative 1 because the
LHS cannot take a negative value
In the second example, we notice that the
LHS has two log symbols while the RHS has only
one.
We start with eliminating the log symbol on
the LHS from log base 9
To do that, we need to come out with a log
base 9 on the RHS
So, we simplify the RHS until we get a constant.
Then, multiply the constant with log base
9 9 because log base 9 9 is just one
Next, bring the fraction 1/2 up to become
the power
Now, we have log base 9 on both sides.
By comparison, log base 3 4x-5 is equal to
9 to the power of 1/2
We repeat the same process again, that is
changing the RHS to log base 3 and compare
again
We have 4x-5 equal to 3 to the power of 3
Solving the equation and we obtain x is equal
to 8
