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
Solving a Logarithmic Equation with Multiple Logs  Problem 1
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!
Solving a logarithmic equation where we have more than one log on the side. Whenever we have a log of equation, where we have more than one log, what we have to do is condense them down together to make a single logarithm. Using our properties of logs, put them back together to get a single log on whatever side has more than one.
For this one here our left side has two logarithms, what we need to do is condense them back down to a single one by subtraction which means that we are dividing when we put it back together, leaving us with x plus 5 over x minus 1 is equal to log base 7 of 3. Now we have the log base 7 of something equals the log base 7 of another thing. Those two things have to be the same, and just knowing that whatever we’re taking the log of has to be the same number so we just drop our logs out and we’re ending up with x plus 5 over x minus 1 is equal to 3.
From here, solving a simple equation, cross multiply, x plus 5 is equal to 3x minus 3. I skipped a step in here I just distributed that 3 in hopefully you can see it. Now we solve for x, let’s take all the x's to one side, everything else to the other side, add 3 over, subtract x and we end up with x is equal to 4.
Whenever we’re solving a logarithmic equation what we have to do is make sure that we can actually take this number and plug it into all of our original statements. So x is equal to 4, we can plug that in we get 9, that’s okay. Plug it in here, 4 minus 1 that’s 3, that’s okay and this log is already 3. So if we ever got a log of a negative number that would tell us that this number wouldn’t actually work, we’d have no solution. In this case we can take 4, we can plug it into all of our logs so we have a solution. Taking our log of equation, condensing everything down to a single log and then we would any other log.
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”
Get Peer Support on User Forum
Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.
Sample Problems (5)
Need help with a problem?
Watch expert teachers solve similar problems.

Solving a Logarithmic Equation with Multiple Logs
Problem 1 9,864 viewsSolve:
log_{7}(x + 5) − log_{7}(x − 1) = log_{7}3 
Solving a Logarithmic Equation with Multiple Logs
Problem 2 7,422 viewsSolve:
log_{2}x + log_{2}(x + 4) = 5 
Solving a Logarithmic Equation with Multiple Logs
Problem 3 6,757 viewsSolve:
log_{2}3 + log_{2}x = log_{2}(x − 2) + log_{2}(x + 2) 
Solving a Logarithmic Equation with Multiple Logs
Problem 4 1,547 views 
Solving a Logarithmic Equation with Multiple Logs
Problem 5 1,425 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete