If log a=2 and log b=3, what is the numerical value of log a

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If log a=2 and log b=3, what is the numerical value of log a^2 over b^3? Please, e-mail the step by step how solution. Thank you!
 
interval said:
Please, e-mail the step by step how solution.
If you are wanting an on-demand private e-mail service that does your homework for you, providing you with completed solutions to hand in, you will need to contract with and pay such a service. But this is not that service.

Here, the volunteers do not generally "do" students' work for them, and all correspondence occurs openly through the forums. Just as you want the tutors to come here and read your questions, so also you need to come here to read the replies.

Meanwhile, your question is ambiguous. I will assume that there is some unnamed base, and that you mean the following:

If log(a) = 2 and log(b) = 3, then what is the numerical value of log(a<sup>2</sup>/b<sup>3</sup>)?
If so, then apply the log rules you've memorized to take the log expression apart. Then plug in the given values, and simplify.

If you get stuck, please reply showing what you have done. Thank you.

Eliz.
 
Re: If log a=2 and log b=3, what is the numerical value of l

Hello, interval!

If \(\displaystyle \,\log a\,=\,2\) and \(\displaystyle \log b\,=\,3\),
what is the numerical value of: \(\displaystyle \,\log\left(\frac{a^2}{b^3}\right)\) ?

You're expected to know the properties of logarithms
. . and know when and how to use them . . .

You have: \(\displaystyle \:\log\left(\frac{a^2}{b^3}\right) \:=\:\log(a^2)\,-\,\log(b^3)\;=\;2\cdot\log(a) \,-\, 3\cdot\log(b)\)

Got it?

 
ok

Yes, Soroban, you are right but I have not seen this log stuff in months.
Logs and exponentials are tricky.
 
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