Question

find this question pls​

Answer 1

Answer:

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

Step-by-step explanation:

$let \: {a}^{x} = {b}^{y} = {c}^{z} = k \\ \\ a = {k}^{ \frac{1}{x} } \: \: \: \: b = {k}^{ \frac{1}{y} } \: \: \: \: \: \: c = {k}^{ \frac{1}{z} } \: (1)$

$\frac{b}{a} = \frac{c}{b} \\ \\ {b}^{2} = ac$

From (1),

${( {k}^{ \frac{1}{x} }) }^{2} = {k}^{ \frac{1}{y} } \times {k}^{ \frac{1}{z} } \\ \\ {k}^{ \frac{2}{x} } = {k}^{ \frac{1}{y} + \frac{1}{z} }$

When bases are same, powers can be equated,

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

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

Hope it helps