Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Evaluating a Logarithmic Expression in terms of Known Quantities  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Often times we will be given information about certain logs and we are supposed to use that information to simplify another statement. What we want to do when we are dealing with that is look to see how the numbers in that statement relate to the numbers that we are given.
So what I see in this case is I have our log base 5 of 4 over 9 I have the log of a quotient so therefore I know that I can break this up as subtraction, so split that 4 and that 9 component up into their own longs. So let's go ahead and of that so we end up with log base 5 of 4 minus log base 5 of 9.
The next thing we need to do is somehow try to express log base 5 of 4 in log base 5 of 9 using log base 5 of 2 or 3. So we have to go back to another property of logarithms which is if we have a power on our log, we can bring that to the outside, so I think about 4. 4 is actually 2 and 2² and 2 we have information about. So what we can do here is just rewrite this as log base 5 of 2² minus log base 5 of 3².
Those exponents we can then bring to the front using our properties of logs, so we end up with 2 log base 5 of 2 minus 2 log base 5 of 3. Now we have information about log base 5 of 2 and log base 5 of 3 already up here, so just simplifying that by plugging those in, this ends up being a 'j', this ends up being a 'k' and we end up with 2j minus 2k.
So using our properties of logs and just what we know about numbers to be able to express fourninths as powers of 2 and powers of 3.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Sample Problems (5)
Need help with a problem?
Watch expert teachers solve similar problems.

Evaluating a Logarithmic Expression in terms of Known Quantities
Problem 1 5,218 viewsGiven log_{5}2 = j and log_{5}3 = k.
Express log_{5}6 in terms of j and k. 
Evaluating a Logarithmic Expression in terms of Known Quantities
Problem 2 4,453 viewsGiven log_{5}2 = j and log_{5}3 = k.
Express log_{5}(4⁄9) in terms of j and k. 
Evaluating a Logarithmic Expression in terms of Known Quantities
Problem 3 4,441 viewsGiven log_{5}2 = j and log_{5}3 = k.
Express log_{5}(15⁄2) in terms of j and k. 
Evaluating a Logarithmic Expression in terms of Known Quantities
Problem 4 1,532 views 
Evaluating a Logarithmic Expression in terms of Known Quantities
Problem 5 1,367 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete