We are all related

Algebra Level 2

$\begin{array} { l l l l l l l } \large & 2^x & = & 3^y & = & 4^z & = & 576 \\ & \frac 1 x & + & \frac 1 y & + & \frac 1 z & = & ? \\ \end{array}$

1 solution

Nelson Mandela
Apr 4, 2015

So, ${ 2 }^{ x }={ 3 }^{ y }={ 4 }^{ z }=576$ .

It can be written as,

$2={ 576 }^{ \frac { 1 }{ x } }$ .

$3={ 576 }^{ \frac { 1 }{ y } }$ .

$4={ 576 }^{ \frac { 1 }{ z } }$ .

so, $2*3*4={ 576 }^{ \frac { 1 }{ x } +\frac { 1 }{ y } +\frac { 1 }{ z } }$ .

So, the required answer is $\log _{ 576 }{ 24 }$ = 0.5.