In the circuit in Figure P9.81, assume that (Q_{1}) and (Q_{2}) are identical transistors. If (T=300 mathrm{~K}),

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In the circuit in Figure P9.81, assume that \(Q_{1}\) and \(Q_{2}\) are identical transistors. If \(T=300 \mathrm{~K}\), show that the output voltage is

\[v_{O}=1.0 \log _{10}\left(\frac{v_{2} R_{1}}{v_{1} R_{2}}\right)\]

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