SOLUTION: Find the number: log lower case5 (1/5)

Question 93358This question is from textbook Algebra and Trigonometry
: Find the number: log lower case5 (1/5) This question is from textbook Algebra and Trigonometry

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You are given a log. Set it equal to y and the problem becomes:
.

.
Change this from logarithmic form to exponential form using the rule:
.
is equivalent to the exponential form
.
By comparing the log format of this rule to your given problem, you can see that a = y, b = 5 because
5 is the base of the given log, and . Substitute these values into their appropriate
position in the exponential form to get:
.

.
Notice on the right side that is equal to . But a number in the denominator
can be moved up into the numerator if you change the sign of its exponent. So you can say
that . That being the case, you can replace with
to make the exponential equation become:
.

.
Notice that 5 is the base on both the left and right sides. So for the two sides to be equal
their exponents must be equal. Therefore, you know that y = -1.
.
Now recall that at the beginning of this problem we said that
.

.
Now we know that y = -1 so that we can write this equation as:
.

.
and that's the answer to the problem.
.
Hope this has helped you a little to understand the problem and how to work it. The ability
to translate from the logarithmic to the exponential form and also from the exponential
form back to the logarithmic form is a useful thing to know. It comes up quite often in
working problems involving logarithms.
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