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 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!
Solving a logarithmic equation where we have more than one log on a single side. Whenever we have more than one log, what we’re always going to have to do is use our properties of logs to condense everything down, once we have a single log we can either put everything into exponential form or know that if we have two logs equal to each other whatever is on the inside has to be the same.
This one, this problem, we’re adding in between our logs, so for condensing that tells us we have to multiply, so we end up with log base 2 of x times x plus 4 is equal to 5. Now we have a single log and a constant on the side, we just need to put everything into exponential form.
I’m going to skip a step, I’m going skip multiplying these that are inside the log and just do it as we put everything into exponential form, so this becomes x² plus 4x is equal to 2 to the 5th, 2 to the 5th, 2, 4, 8, 16, 32, so this ends up being x² plus 4x is equal to 32.
Now we’re solving a quadratic so we brig that 32 around, x² plus 4x minus 32 is equal to zero and factor to solve. So we end up with x plus 8 and x minus 4, leaving us with 8 and +4.
Whenever we’re solving a logarithm equation what we have to do is make sure that our answers actually work in the equation that we started with. What I mean by work is do they actually go in and are they actually in the domain? Remember we can’t take the log of a negative number. So when we take 8, plug this in, we can’t take the log of a negative number and we’re left with the log base 2 of 8. That’s not going to work. So 8 is actually an extraneous solution, it’s not going to work.
Now we need to try the same thing with 4. Log base 2 of 4, that’s fine, log base 2 of 8, that’s fine, so that actually works. So go back and check, one of our solutions ends up working, one of them doesn’t, but by condensing our two logarithms down to 1, we were able to solve this logarithmic equation.
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.

Solving a Logarithmic Equation with Multiple Logs
Problem 1 10,137 viewsSolve:
log_{7}(x + 5) − log_{7}(x − 1) = log_{7}3 
Solving a Logarithmic Equation with Multiple Logs
Problem 2 7,916 viewsSolve:
log_{2}x + log_{2}(x + 4) = 5 
Solving a Logarithmic Equation with Multiple Logs
Problem 3 6,942 viewsSolve:
log_{2}3 + log_{2}x = log_{2}(x − 2) + log_{2}(x + 2) 
Solving a Logarithmic Equation with Multiple Logs
Problem 4 1,657 views 
Solving a Logarithmic Equation with Multiple Logs
Problem 5 1,514 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete