How to solve log equations?
#1. log _{x}125 = log _{8}x^3 #
#2. log x^2 = log _{2x}25#
#3. log _{15}x = log _{5}3x#
2 Answers
Generally, it helps to reduce both sides to a common base.
Explanation:
There is no overall answer to this question. Some log equations are best solved by a range of methods. However, in general, it usually helps to reduce both sides to a common base.
To demonstrate this I will solve your question 1.
Let's reduce both sides to
Remember
NB: This approach can be used on the other two problems. In Q2 you will need to assume a base for the LHS - I suggest 10, but it must be stated for the solution to be valid.
(1)
Explanation:
(1) As
or
i.e.
or
=
i.e.
and
(2)
i.e.
or
or
and
=
=
=
Hence.
(3)
i.e.
or
or
or
i.e.
Hence