# Logarithims and Exponents

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If the amplitude ratio, N in decibels, of an electrical system is given by the formula;-

N=10log(Po [output]/Pi [input])

and the power is given by;-

P=V^2/R

Show that for matched input and output resistances the output voltage V[output] is related to V[input] by ;-

Vo[output]=Vi [input] 10^(N/20)

If N is increased by 6dB, show that the output voltage is approximately doubled for the same input.

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