SOLUTION: write the logarithmic equation in exponential form:
log 3 27 = 3
and
log 125 25 = 2/3
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Question 70516: write the logarithmic equation in exponential form:
log 3 27 = 3
and
log 125 25 = 2/3
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If the log form is log b (d) = c
.
(read that as log to the base b of d equals c)
.
then the corresponding exponential form is
.
You are given log 3 (27) = 3. By comparing this with the log form (see top line above) you can
see that b = 3, d = 27, and c = 3. Putting these numbers in the appropriate places in the
exponential form results in:
.
Note that this equation is true because if you cube 3 you get 27
.
You are also given log 125 (25) = 2/3. By again comparing this with the log form in the first
line of this reply, you see that b = 125, d = 25, and c = 2/3. Substituting these numbers
for their corresponding letters in the exponential form results in:
.
.
You may recognize that the exponent means that you can either square the number and
then take the cube root, or you can take the cube root and then square that number.
In the case of 125, it is easier to first take the cube root because it is 5, and then
you square that to get 25. This means the exponential form is true because the left side
of that equation equals the right side.
.
If you work a number of these, you will see the pattern between the log and exponential
forms and the translation back and forth between the two forms will become easier for you.
Hope this helps you see your way through this type of problem.
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