Solving Logarithmic Equations with Given Logs

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Homework Help Overview

The discussion revolves around solving logarithmic equations using given logarithmic values for specific numbers. The participants are exploring how to apply logarithmic properties to find values for loga(130), loga(1.3), and loga(1000).

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the logarithm of a product and the logarithms of its factors. There is an exploration of how to express loga(130) using loga(10) and loga(13). Some participants express confusion about the operations involved, particularly regarding addition and multiplication of logarithmic values.

Discussion Status

Some participants have provided guidance on using logarithmic rules, such as the product rule. There is a recognition of the need to express numbers in terms of known logarithmic values, and some participants have indicated they are beginning to understand the process, while others still express confusion.

Contextual Notes

Participants mention missing information from a previous class and express uncertainty about the application of logarithmic rules. There is a focus on understanding how to manipulate logarithmic expressions without providing complete solutions.

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Homework Statement


1. Use the fact that loga(10)= 2.4197 and loga(13)=2.6955 to solve the following

a. loga(130) b. loga(1.3) c. loga(1000)

Homework Equations





The Attempt at a Solution


I'm not really sure how to do this i missed yesterdays class i don't really want the anwser just some help on how to do it because i don't understand it out of the book at all. any help would be greatly appreciated
 
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Do you know some rules of logarithms? Like 130=13*10. How is the log of a product related to the log of the terms?
 
well i think you getting at something like this
so if i have logam+logan

i get loga(m)(n)
 
Everstar said:
well i think you getting at something like this
so if i have logam+logan

i get loga(m)(n)

Sure. log_a(m)+log_a(n)=log_a(m*n). So what's the answer to the first one?
 
well I'm not sure if I am correct but i multiplied the two numbers 2.4197*2.6955 = 6.522
 
Everstar said:
well I'm not sure if I am correct but i multiplied the two numbers 2.4197*2.6955 = 6.522

Why did you multiply them? If log_a(m)+log_a(n)=log_a(mn) and you put m=10 and n=13, I don't think you want to multiply 2.4197*2.6955.
 
well then i just get log_a(10)(13) which is 130 but i don't understand what i am supposed to do with that? I am sorry I am just confused
 
Everstar said:
well then i just get log_a(10)(13) which is 130 but i don't understand what i am supposed to do with that? I am sorry I am just confused

What do you think log_a(10)(13) means? You are a little too confused. Look, log_a(10)+log_a(13)=log_a(10*13)=log_a(130). You know log_a(10)=2.4197 and log_a(13)=2.6955. I wouldn't multiply them.
 
oh my goodness lol i add them =)
 
  • #10
Everstar said:
oh my goodness lol i add them =)

Thank you. Yes. Now express 1.3 and 1000 in terms of 10 and 13 and use the rules of logs again.
 
  • #11
i figured it out thank you for the help =) i add the first one then divide (subtract the second one, then add add add on the third one. thanks =)
 
  • #12
Everstar said:
i figured it out thank you for the help =) i add the first one then divide (subtract the second one, then add add add on the third one. thanks =)
Yes, log(1000)= log(10*10*10)= log(10)+ log(10)+ log(10). Of course, that's the same as 3*log(10). That's another "rule of logarithms": log(xy)= y log(x).
 

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