Question

Given 3x = 4y = 12z, show that z = xy/(x + y)
.

Answer 1

can u give me a minute?

Answer 2

oops \[3^x=3^y=12^z z=\frac{xy}{x+a} \]

Answer 3

x+y

Answer 4

let:

\[3^x = 4^y = 12^z = k\]

\[3 = k^{1/x}\]

\[4 = k^{1/y}\]

\[12 = k^{1/z}\]

Use:

\[3 \times 4 = 12\]

\[k^{1/x} \times k^{1/y} = k^{1/z}\]

\[\implies \frac{1}{x} + \frac{1}{y} = \frac{1}{z}\]

\[\frac{1}{z} = \frac{x + y}{xy}\]

\[\implies \color{blue}{z = \frac{xy}{x+y}}\]

Answer 5

wow @waterineyes u r faster than me

Answer 6

How??

Answer 7

when i solved it u already posted the solution

Answer 8

ohh can u solve using log?

Answer 9

I can try..