Solving Logarithmic Equations with Given Logs

[Everstar]

Homework Statement

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

a. log_a(130) b. log_a(1.3) c. log_a(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 becuase i don't understand it out of the book at all. any help would be greatly appreciated

 

[Dick]

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?

 

[Everstar]

well i think you getting at something like this
so if i have log_am+log_an

i get log_a(m)(n)

 

[Dick]

well i think you getting at something like this
so if i have log_am+log_an

i get log_a(m)(n)

Sure. log_a(m)+log_a(n)=log_a(m*n). So what's the answer to the first one?

 

[Everstar]

well I'm not sure if I am correct but i multiplied the two numbers 2.4197*2.6955 = 6.522

 

[Dick]

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.

 

[Everstar]

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

 

[Dick]

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.

 

[Everstar]

oh my goodness lol i add them =)

 

[Dick]

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.

 

[Everstar]

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 =)

 

[HallsofIvy]

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(x^y)= y log(x).