Question

if 2^x=4^y=8^z,then find the value of x:(y+z)

Answer 1

Step-by-step explanation:

x=6

y=4

z=2

x:(y+z)=6:(4+2) ans

Answer 2

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QueStI0N -

If ${2}^x={4}^y={8}^z,$ then find the value of [ xy ] / [ x + y ]

S0LUTION -

${2}^x={4}^y={8}^z = k \\ \\ => 2 = {k} ^ { \frac{1}{x} } \\ \\ => 4 = {k} ^ { \frac{1}{y} } \\ \\ => 8 = {k} ^ { \frac{1}{z} } \\ \\ 2 \times 4 = 8 \\ \\ => {k} ^ { \frac{1}{x} } \times {k} ^ { \frac{1}{y} } = {k} ^ { \frac{1}{z} } \\ \\ => {k} ^ { \frac{1}{x} + \frac{1}{y} } = {k} ^ { \frac{1}{z} } \\ \\ => \dfrac{ 1}{ x } + \dfrac{1}{ y } = \dfrac{1}{ z } \\ \\ => \dfrac{ x+y}{ xy } =. \dfrac{ 1}{ z} \\ \\ => \dfrac{xy}{x+y} = z ....... [ A ]$

Using the relation between x , y and z , you can find any value in the ratio of x, y and z .