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

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Homework Help Overview

The problem involves solving a logarithmic equation where the arguments of the logarithms are set equal to each other due to having the same base. The context is within the subject area of logarithmic properties.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the validity of setting the arguments of the logarithmic functions equal to each other and explore the implications of the resulting equation. There is a consideration of the graphical representation of the functions involved, noting their parallel nature.

Discussion Status

The discussion has led to the conclusion that there is no solution to the equation based on the reasoning that the arguments cannot equal each other. Participants have acknowledged this outcome, although the exploration of the problem remains open-ended.

Contextual Notes

Participants note that the expressions represent horizontal shifts of each other, which contributes to the understanding that they do not intersect, reinforcing the conclusion of no solution.

KatieLynn
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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...
 
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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
 
so that means there is no answer?
 
yep...
 
KatieLynn said:
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...)
 

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