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  Concept
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!
Just as we can use logarithms to access exponents in exponential equations, we can use exponentiation to access the insides of a logarithm. Solving logarithmic equations often involves exponentiating logarithms in order to get rid of the log and access its insides. Sometimes we can use the product rule, the quotient rule, or the power rule of logarithms to help us with solving logarithmic equations.
Solving simple logarithm equations and what I mean by simple logarithm equations is actually ones that we have a single log and one or both sides so we only have a maximum of two logs one on the right one on the left and basically what what we do in these situations is put the equation into exponential form and then solve it up. The one thing we really have to be careful about is our domain and remember that we can't take the log of a negative number so whenever we get an answer we always have to check.
Okay so behind me I have a pretty straight forward example log base 4 of x3 is equal to 2 okay? To solve this out all we want to do is put this into exponential form so we bring the 4 up and around leaving us with x3 is equal to 4 squared, 4 squared is 16, x3=16 add 3 to both sides leaving us with x=19 okay? Now the last thing we have to do is check make sure this actually can go into our equation, we plug 19 in, 193 is 16 log base 4 of 16 is in fact 2 okay? so whenever we're solving a logarithm equation, we're only having one or two logs just put an exponential form and solve.
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.
Concept (1)
Sample Problems (6)
Need help with a problem?
Watch expert teachers solve similar problems.

Solving a Logarithmic Equation
Problem 1 8,555 viewsSolve:
log_{3}(x² + 10x + 25) = 4 
Solving a Logarithmic Equation
Problem 2 7,311 viewsSolve:
2log_{4}(3x − 2) = 6 
Solving a Logarithmic Equation
Problem 3 6,698 viewsSolve:
log_{7}(5 − x) = log_{7}8 
Solving a Logarithmic Equation
Problem 4 1,228 views 
Solving a Logarithmic Equation
Problem 5 1,216 views 
Solving a Logarithmic Equation
Problem 6 1,066 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete