Answer
$1$
Work Step by Step
$ Average=\dfrac{1}{(ln 2)^2} \int_{\ln 2}^{2 \ln 2} \int_{\ln 2}^{2 \ln 2} \dfrac{1}{xy} \space dy \space dx $
or, $=\dfrac{1}{(ln 2)^2} \int_{ln 2}^{2 ln 2}[\dfrac{ln y}{x}]^{2ln2}_{ln2} \space dx $
or, $=\dfrac{1}{(ln2)^2}\int_{ln 2}^{2 ln 2}\dfrac{1}{x}(\ln 2+\ln \ln (2)-\ln \ln (2)]dx $
or, $=\dfrac{1}{\ln (2)}\int_{ln 2}^{2 \ln (2) }dx $
or, $=\dfrac{1}{\ln2}(\ln 2+ln [ln (2)]-\ln [ln(2)])$
or, $=1$
