Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.3 Logarithmic Functions - 4.3 Exercises - Page 447: 104

(a) $9$ (b) $ -6$ (c) $ -20$ (d) $ 125$

(a) As $a^{log_ax}=x$, we have $100^{log_{10}3}=(10^2)^{log_{10}3}=10^{2log_{10}3}=10^{log_{10}3^2}=9$ (b) $log_{10}(0.01)^3=log_{10}(10^{-2})^3=-6$ (c) $log_{10}(0.0001)^5=log_{10}(10^{-4})^5=-20$ (d) $1000^{log_{10}5}=(10^3)^{log_{10}5}=10^{3log_{10}5}=10^{log_{10}5^3}=125$