Question

3x=5y=(75)z find the relation among x,y,z
PLEASE ANSWER FAST IT IS EXTREMELY URGENT!!!!

Answer 1

/(2x + y)

3^x = 5^y = 75^z

Take log,

x log3 = y log5 = z log75 = k

log 3 = k/x 5 = k/y

z = k/(log 25 ×3)

z = k/(2 log5 + log3)

z = k/{2(k/y) + (k/x)}

z = xy/(2x + y)

Answer 2

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• If $\sf {3}^{x} = {5}^{y} = {75}^{z}$, then find the relation between x, y and z.

$\star\:\:\:\sf\large\underline\blue{Solution:-}$

Given,

$\sf {3}^{x} = {5}^{y} = {75}^{z}$

$\sf let \: {3}^{x} = {5}^{y} = {75}^{z} = k$

Therefore,

$\sf {3}^{x} = k \implies3 = {k}^{ \frac{1}{x} }$

$\sf {5}^{y} = k \implies5 = {k}^{ \frac{1}{y} }$

$\sf {75}^{z} = k \implies75 = {k}^{ \frac{1}{z} }$

Again,

$\sf 75 = 3 \times {5}^{2}$

$\sf \implies {k}^{ \frac{1}{z} } = {k}^{ \frac{1}{x} } \times {k}^{ \frac{2}{y} }$

Comparing base, we get,

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

This is the relationship between x, y and z, i.e.,

$\boxed{ \sf \frac{1}{z} = \frac{1}{x} + \frac{2}{y} }$