Write in simplified form 2log x+log y-3logz
do you know properties of logarithm?? like this log a + log b = log (a*b)
Yes I do
use this property first: \(\large log_b(x^y)=ylog_b(x) \)
How do I plug that in
then use the product to sum and quotient to difference properties.
in your first term, \(\large 2logx=log(x^2) \) can you do that with the third term in your equation?
Log(z^3)?
yes... @hartnn , sorry, i didn't mean to hijack the problem.... do you want to continue this?
no u didn't hijack.....u please continue :)
ok... thanks.... :)
sorry haley.... chrome crashed on me....:(
That's quite alright! :)
so now your expression is: \(\large log(x^2)+logy-log(z^3) \) now can you do the sum to product and difference to quotient rules for logs from here?
It's new material so I'm not very familiar with it. How do I begin?
here are the properties: \(\large log_bx + log_by = log_b(x\cdot y) \) and \(\large log_bx - log_by = log_b(\frac{x}{y}) \)
Ugh so lost I'm still not quite sure how to plug those in to solve
ok... i shouldn't have used x's and y's in the properties because your equation uses the same variables..... lemme try again....
Ohh ok
What did you get for your answer? I got logx+logz never mind.. that can't be right
this is your expression: \(\large log(x^2) +logy - log(z^3) \) applying the sum to product property on the first two terms we get: \(\large \color {red}{log(x^2) +logy} - log(z^3) \) \(\large \color {red}{log(x^2\cdot y)} - log(z^3) \) still with me?
Yess
now applying the difference to quotient property of logs on the remaining terms to simplify we get: \(\large log(x^2\cdot y) - log(z^3) \) \(\large log(\frac{x^2\cdot y}{z^3} ) \)
So that's the simplifed expression o.O
I got something completely different lol. But you really helped out.
yep... your original expression was expressed in terms of 3 logs this one has 1...
what did you get?
i think i'm correct... lemme check...
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