SOLUTION: I'm trying to convert this equation: log base 100 (1/100x). I got to Log base 100 (1) - log base 100 (100x) but I don't know the missing steps to get to: -1-log (sqrt of x)

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Question 270396: I'm trying to convert this equation: log base 100 (1/100x). I got to Log base 100 (1) - log base 100 (100x) but I don't know the missing steps to get to: -1-log (sqrt of x)
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!

You are correct so far. To continue we can first simplify the first logarithm. Since . So now we have

Now we can use the property of logarithms, to separate the remaining log into two:

Note the use of parentheses. Whenever you substitute one expression for another, especially when there are a different number of terms, it is a very good idea to use parentheses like this. In this case, it helps us understand that the "-" in front applies to both terms.
The first log is 1 so

At this point we have the -1 part of the answer. The other term in the answer is a base 10 logarithm, not a base 100 logarithm. So we need to change the base of our remaining logarithm using the formula: . Using this to change our base 100 logarithm into a base 10 logarithm we get:

And since :

We're getting close. We have the -1 and we have the base 10 logarithm. We only have to figure out how . Since dividing by 2 is the same as multiplying by 1/2 we can rewrite the term as a multiplication:

Now we can use the property of logarithms, to move the 1/2 into the argument as an exponent:

And since an exponent of 1/2 means square root:

And we're done!