Question

if 2^x=3^y=6^z then z is equal to

Answer 1

Answer:

Zero

Step-by-step explanation:

Given 2^x=3^y=6^-z. Thus 1/z will be equal to - log 6 to base k. Which will be equal to log 6 to base k - log 6 to base k. Thus makes the whole equation equal to zero.

Answer 2

$z=\frac{x}{log 3}$ and $z=\frac{y}{log 2}$

Step-by-step explanation:

According to the question $2^x=3^y=6^z$

OR we can write

$2^x=6^z$

$log2^x=log6^z$

$loga^b = bloga$

$xlog2=zlog6$

$xlog2=zlog(2\times3)$

$\frac{x}{z}=\frac{log(2\times3)}{log2}$

$\frac{x}{z}=log 3$

$z=\frac{x}{log 3}$

• Similarly solving the other part

$3^y=6^z$

$log3^y=log6^z$

$ylog3=zlog6$

$ylog3=zlog(2\times3)$

$\frac{y}{z}=\frac{log(2\times3)}{log3}$

$\frac{y}{z}=log 2$

$z=\frac{y}{log 2}$