I am really struggling to find the answer to this logarithmic equation that we have been set:
Divide through by 2 since all coefficients are even:
Write as
Multiply through by to clear of fractions:
Simplify:
Replace by
Swap the second and third term on the left to get
in descending order or powers of
Factor the left side:
Set each factor = 0
For each solution for u, replace by
For ,
Take logs of both side:
Use the principle of logs on the left that]
allows you to move an exponent in front of
the log:
Divide both sides by
Use your calculator:
For ,
Multiply through by 3 to clear of fractions:
Write as
Add exponents on the left:
Write the on the right as
Since the bases are both the same, and positive
and not equal to 1, we may equate the
exponents:
So there are two solutions,
and
Edwin