Not sure how to do this?
Use log5 2 = .4307 and log5 3=.6826 to approximate the value of each expression. log5 30

Question

Not sure how to do this?
Use log5 2 = .4307 and log5 3=.6826 to approximate the value of each expression. log5 30

unknownrandom · Answer

@satellite73

mathmale · Answer

First:  What is log 10?  (Note:  the base is 10)
           What is the value of $$\log_{5} 5=\log_{5}5^1? $$

Supposing that we now have:
$$\log_{5}2=0.4307 ,~\log_{5}3 =0.6826~and~\log_{5} 5=1.0000$$  Now we're ready to find $$\log_{5}30. $$
Ask yourself:  How would you use the factors 2, 3 and 5 to obtain 30?

Note: 2*3 = 6, right?
Therefore, $$\log_{5} 3+\log_{5}2=\log_{5}6  $$   think about this.  If you know how to make use of the factors 2, 3 and 5 to obtain 30, then you can use a similar approach to find $$\log_{5}30 $$

unknownrandom · Answer

Thanks @mathmale! I think I understand now. I got 2.1133.

mathmale · Answer

You've done very well!!

Try this on your calculator:  5^2.1133.  What do you get?  What does that tell you?

unknownrandom · Answer

I got 30.

unknownrandom · Answer

So they balance out. I am not sure what it tells me though?

unknownrandom · Answer

I know the answer is valid because they equal the same thing. Is that what you are asking?

mathmale · Answer

Exactly.  You have correctly found the exponent of 5 that produces 30.  Nice work!!

unknownrandom · Answer

I have a question on this one log5 (2/3)

mathmale · Answer

That's the log of a quotient.  The rule of logs for that is $$\log \frac{ a }{ b }= \log a - \log b$$, or the other way around:  Can you apply tht rule to your "log5 (2/3)?"