Question 1138924: Hi! i have a test tomorrow on logs and i am having trouble knowing how to evaluate a log without a calculator for example these are some of the problems i am having trouble with.....
log base 9 of (1/3)
log base 8 of 19
and log base 3 of 27 - log base 3 of 9
Answer by ikleyn(52806)   (Show Source):
You can put this solution on YOUR website! .
1)  .
Ask yourself, to which degree should you raise the number "9" to get the number  ?
Clearly, you should take the square root of 9, which is  = 9^(1/2) = 3, and then invert it, getting .
So, 9^(1/2) = 3, which means that =  .
2)  -  = 3 - 2 = 1,
simply because  = 3 and  = 2.
3)  can not be simplified.
If the teacher / textbook / exam asks you evaluate it, use your calculator to get a numerical value.
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On logarithms and their properties, see the lessons
- WHAT IS the logarithm
- Properties of the logarithm
- Change of Base Formula for logarithms
- Solving logarithmic equations
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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It is not very good strategy to come to the forum with such questions at the day before exam (at the evening or even night before it).
Had you come earlier, you would learn much more from this forum.
Probably, the first thing which you should know firmly is the DEFINITION of the logarithm.
Learn it from the very first lesson of my list.
I wish you to solve all your problems at the exam successfully !
Come again to the forum soon . . . (!) . . . for new knowledge !
And to get them in time !
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