Math: log question-solving for x.

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Homework Help Overview

The discussion revolves around solving a logarithmic equation involving the variable x, specifically in the context of logarithms with a base of 6.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to manipulate the logarithmic terms but expresses uncertainty about their approach and whether they have multiplied correctly. Some participants suggest using logarithmic properties to combine terms and clarify the relationship between logarithms and their arguments.

Discussion Status

Participants are exploring different methods to approach the problem, with some providing guidance on logarithmic rules. There is acknowledgment of the need for x to meet certain conditions to avoid undefined terms, indicating a productive direction in the discussion.

Contextual Notes

It is noted that x must be positive and greater than 5, which is crucial for the validity of the logarithmic expressions involved.

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Homework Statement


Solve: log(sub6)x+log(sub6)(x-5) = 2


Homework Equations



na?

The Attempt at a Solution



i multiplied the second log out and got:
log(sub6)x+log(sub6)x-log(sub6)5 = 2
then i put the x's on one side and the numbers on the other.
2(log(sub6)x) = 2+log(sub6)5

but i have no idea how to go from there. or maybe i multiplied it out wrong?
 
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Instead of doing all of that use this rule

logAa+logAb=logA(ab)

and then use the fact that logAa=n ⇒ a=An
 
https://www.physicsforums.com/attachment.php?attachmentid=22534&stc=1&d=1260947038
Try to understand each steps that i proceed.
 

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Ah! I see now, thank you both so much!
 
Remember that from your original equation x has to be positive and x has to be greater than 5 (which together mean that x > 5). Otherwise one of the terms in your original equation will be undefined.
 

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