Here's the question you clicked on:
vivalakoda
I need help with an IMPOSSIBLE equation?
Well what is it?...
3 log 2 x + 1/2 log 2 y – 3 log 2 z = log 2 (x^3√y / z^3).
Nothing is impossible.
Okay, that's an impossible equation indeed. But it has multiple solutions.
Exaggeration of course, ha
So it is capable of being solved? I could call it true?
Yes, it can be solved by using these identities:\[\log_a b + \log _a c = \log_a (bc)\]and\[\log_a b - \log_a c = \log_a (b/c)\]
\[\log_2x^3+\log_2y^{1/2}-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]
Two more:\[a\log b = \log b^a\]and\[\log_a b = \log_a c \iff b = c\]
now i think it's possible now
I am very, very lazy and I am very, very serious about that. So I think @jiteshmeghwal9 will continue helping :-p
It asks me if the equation is true, and if so then to explain the properties used. o.o
The identities I listed.
Use them one-by-one.
\(log_2x^3+log_2(y^{1/2})=log_2(x^3\sqrt{y})\) now \(log_2(x^3\sqrt{y})-log_2z^3=log_2(x^3\sqrt{y}/z^3)\)
That's it, right there. ^
\[\log_2x^3+\log_2y^{1/2}-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]since\[\log_2x^3+\log_2(y^{1/2})=\log_2(x^3\sqrt{y})\]\[\log_2(x^3\sqrt{y})-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]so,\[\log_2(x^3\sqrt{y}/z^3)=\log_2(x^3\sqrt{y}/z^3)\]H.P.
Brotip: Use Q.E.D. instead of H.P. :-)
I am so confused. Thank you everyone for the help, I'll just do my best to take the identities you both listed and write something about it. Very much appreciated!
yw :) Best of luck;)
By properties they mean the logarithmic properties :c I just asked my teacher. So the power property, the product property, and the quotient property? Would any of those fit?
Power Property \[\log a^b=b \log a\] Product Property \[\log ab= \log a +\log b \] Quotient property \[\log \dfrac{a}{b}=\log a - \log b\]
\(blog_ac=log_ac^b\) \(log_ab+log_ac=log_abc\) \(log_ab - log_ac=log_a\dfrac{b}{c}\)
these are the only properties used in the question
How do they show that the equation is true, though?
I have proved this above