SOLUTION: Can;t remember if I ask this or not - but will ask again - THANK YOU How do i wrtie the following in exponential form log2 16 = 4 log2 125 = 3 and how to I write the fo

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Can;t remember if I ask this or not - but will ask again - THANK YOU How do i wrtie the following in exponential form log2 16 = 4 log2 125 = 3 and how to I write the fo      Log On

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Question 93117: Can;t remember if I ask this or not - but will ask again - THANK YOU
How do i wrtie the following in exponential form
log2 16 = 4
log2 125 = 3
and
how to I write the following in logarithmic form
10^-1 = 0.1
thanks
Lucy

Found 2 solutions by Nate, bucky:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
log2 16 = 4
~ 16 = 2^4
log2 125 = 3
~ 125 = 2^3 should be 5^3
..................................
10^-1 = 0.1
-1 = log10 0.1
-1 = log 0.1

Answer by bucky(2100) About Me  (Show Source):
You can put this solution on YOUR website!
The rule is as follows:
.
log%28a%2Cb%29+=+y is equivalent to a%5Ey+=+b
.
So in log%282%2C16%29+=+4 a = 2, b = 16, and y = 4. Therefore, the equivalent exponential
form is 2%5E4+=+16
.
Your next problem has a typo or your source of the problem is trying to see if you can catch
the error. You are given that log%282%2C125%29+=+3. In this form a = 2, b = 125, and y = 3,
so the "equivalent" exponential form is 2%5E3+=+125. But notice that this is not true.
The original problem should be log%285%2C125%29+=+3. The equivalent exponential form is
then 5%5E3+=+125 and this is true.
.
Finally you are given the exponential form 10%5E%28-1%29+=+0.1 and are asked to convert it
to logarithmic form. By comparing this given with the exponential rule, you can see that
a = 10, b = 0.1, and y = -1. Substituting these into the logarithmic rule you get the
equivalent form log%2810%2C+0.1%29+=+-1.
.
Hope this helps you to understand this conversion process.