Question

if 4 to the power x 4 to the power x is equals to a to the power Y is equals to 16 ^ Z show that 2 by Y is equal to 1 by X + 1 by Z ​

Answer 1

Step-by-step explanation:

$Given: \: {4}^{x} = {8}^{y} = {16}^{z} \\ \implies \: {2}^{2x} = {2}^{3y} = {2}^{4z} \\ \implies \: 2x = 3y = 4z \\ \implies \: 2x = 3y \\ \implies \: x = \frac{3y}{2} \\ \implies \: 4z = 3y \\ \implies \: z = \frac{3y}{4} \\ now \\ RHS = \frac{1}{x} + \frac{1}{z} = \frac{1}{ \frac{3y}{2} } + \frac{1}{ \frac{3y}{4} } \\ = \frac{2}{3y} + \frac{4}{3y} \\ = \frac{2 + 4}{3y} \\ = \frac{6}{3y} \\ = \frac{2}{y} \\= LHS \\ Thus \\ \frac{1}{x} + \frac{1}{z} = \frac{2}{y} \\or \\</p><p>\frac{2}{y}=\frac{1}{x} + \frac{1}{z}\\ Hence proved.$