Question

I need help with an IMPOSSIBLE equation?

Answer 1

Well what is it?...

Answer 2

3 log 2 x + 1/2 log 2 y – 3 log 2 z = log 2 (x^3√y / z^3).

Answer 3

Nothing is impossible.

Answer 4

Okay, that's an impossible equation indeed. But it has multiple solutions.

Answer 5

Exaggeration of course, ha

Answer 6

So it is capable of being solved? I could call it true?

Answer 7

Yes, it can be solved by using these identities:\[\log_a b + \log _a c = \log_a (bc)\]and\[\log_a b - \log_a c = \log_a (b/c)\]

Answer 8

\[\log_2x^3+\log_2y^{1/2}-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]

Answer 9

Two more:\[a\log b = \log b^a\]and\[\log_a b = \log_a c \iff b = c\]

Answer 10

now i think it's possible now

Answer 11

I am very, very lazy and I am very, very serious about that. So I think @jiteshmeghwal9 will continue helping :-p

Answer 12

o_O

Answer 13

It asks me if the equation is true, and if so then to explain the properties used. o.o

Answer 14

The identities I listed.

Answer 15

Use them one-by-one.

Answer 16

\(log_2x^3+log_2(y^{1/2})=log_2(x^3\sqrt{y})\)

now \(log_2(x^3\sqrt{y})-log_2z^3=log_2(x^3\sqrt{y}/z^3)\)

Answer 17

That's it, right there. ^

Answer 18

\[\log_2x^3+\log_2y^{1/2}-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]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.

Answer 19

Brotip: Use Q.E.D. instead of H.P. :-)

Answer 20

Q.E.D=?

Answer 21

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!

Answer 22

yw :)

Best of luck;)

Answer 23

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?

Answer 24

Power Property

\[\log a^b=b \log a\]

Product Property

\[\log ab= \log a +\log b \]

Quotient property

\[\log \dfrac{a}{b}=\log a - \log b\]

Answer 25

\(blog_ac=log_ac^b\)
\(log_ab+log_ac=log_abc\)
\(log_ab - log_ac=log_a\dfrac{b}{c}\)

Answer 26

these are the only properties used in the question

Answer 27

How do they show that the equation is true, though?

Answer 28

I have proved this above