Question

please give me correct answer please ​

Answer 1

$\huge\mathfrak\pink{question}$

${2}^{x} = {10}^{y} = {50}^{z}$

$\huge\mathfrak\pink{To \: Find}$

$y \: = \frac{2xz}{x + z}$

$\huge\mathfrak\pink{Solution}$

They will be equal to constant value 'a'

${2}^{x} = {10}^{y} = {50}^{z} = a \:$

${2}^{x} = a \:$

$2 = {a}^{ \frac{1}{x} }$

$\rule{7cm}{0.005cm}$

${10}^{y} = a$

$10 = {a}^{ \frac{1}{y} }$

$\rule{7cm}{0.005cm}$

${50}^{z } = a$

$50 = {a}^{ \frac{1}{z} }$

$\rule{7cm}{0.005cm}$

${a}^{ \frac{1}{y} - \frac{1}{x} } = \frac{10}{2}$

${a}^{ \frac{1}{y} - \frac{1}{x} } = 5 - - - - - - (1)$

$\rule{7cm}{0.005cm}$

Now ,

10 × 5 = 50

: \implies

$: \implies{a}^{ \frac{1}{y} } \times {a}^{ \frac{1}{y} - \frac{1}{x} } = {a}^{ \frac{1}{z} }$

$: \implies {a}^{ \frac{2}{y} - \frac{1}{x} } = {a}^{ \frac{1}{z} }$

$: \implies\frac{2}{y} - \frac{1}{x} = \frac{1}{z}$

$: \implies \frac{2}{y} = \frac{1}{x} + \frac{1}{z}$

$: \implies\frac{2}{y} = \frac{x + z}{xz}$

$: \implies \: y = \frac{2xz}{x + z}$