Question

Please give me these answer step by step then I will mark you as brainliest​

Answer 1

• Step-by-step explanation:
• Q15 seems interesting I will do that....

let

${a}^{x } = {b}^{y } = {c}^{z} = k$

Therefore

$a = {k}^{ \frac{1}{x} } \\ b = {k}^{ \frac{1}{y} } \\ c = {k}^{ \frac{1}{z} }$

Given

${b}^{2} = ac$

Therefore we can say

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

So

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

Loging both sides we have

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

So

$\frac{2}{y} ( log_{a}(k) ) = \frac{1}{x} + \frac{1}{z}( log_{a}(k) )$

Canceling logs on both sides we get

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

Hence Proved..

Mark this answer as brainliest as it was a Pain writing these variable in maths format