Solving Log Equations: How to Use Logarithmic Properties | Homework Help

[KatieLynn]

Homework Statement

Solve the equation
log base 7 (7x+8) = log base 7 (7x+3)

Homework Equations

I don't think you use equations for this, just the properties of logarithms

The Attempt at a Solution

I thought since they have the same base you could set the parts in parenthesis equal to each other

(7x+8) = (7x+3)

so you get
8=3 or
5=0

but that can't be right...

 

[rock.freak667]

Well that should be correct...but if you knew what the graphs looked like, you would see that they are just horizontal shifts of each other...so it is kind of like they are "parallel' or so to say...meaning that they do not intersect

 

[KatieLynn]

so that means there is no answer?

 

[rock.freak667]

yep...

 

[dynamicsolo]

so that means there is no answer?

You correctly remarked that if the expressions on both sides of the equation use the same base for the logarithm, then the arguments of the log functions on each side must be equal. So, if you typed this correctly, that would be asking for the value of x such that 7x + 8 = 7x + 3 . You also observed that there is no such value possible. So that is your answer: there is no solution to this equation. (That can happen occasionally in a homework or exam problem, or in Real Life. Demonstrating that a solution doesn't exist can be just as meaningful as finding a solution...)