Question

if 5 ka power X equal to 3 ka power X equal to 45 ka powerz then prove that 1 by Z equal to 1 by X + 2 by Y​

Answer 1

Step-by-step explanation:

$Given \: it \\ {5}^{x} = {3}^{y } = {45}^{z} = k(say) \\ taking \: log \: on \: both \: sides \\ log {5}^{x} = logk \\ x = \frac{logk}{log5} \\ thus \:, we \: can \: say \: that \\ y = \frac{logk}{log3} \: \: \: \:, \: \: \: z = \frac{logk}{log45} \\ according \: to \: question \\ \frac{1}{x} + \frac{2}{y} = \frac{log5}{logk} + \frac{2log3}{logk} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{log5 + log9}{logk} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{log45}{logk} \: \: \: \: \: \: \: \: \: \: \: (using \: logm + logn = logmn) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{z } \\ hence \: proved \\ hope \: it \: will \: help \: you. \:$