## University Calculus: Early Transcendentals (3rd Edition)

(a) $2^{\log_23}=3$ (b) $10^{\log_{10}\frac{1}{2}}=\frac{1}{2}$ (c) $\pi^{\log_{\pi}7}=7$ (d) $\log_{11}121=2$ (e) $\log_{121}11=\frac{1}{2}$ (f) $\log_3\frac{1}{9}=-2$
*For (a) to (c): Use the first inverse property with base $a$: $$a^{\log_a x}=x$$ Therefore: (a) $$2^{\log_23}=3$$ (b) $$10^{\log_{10}\frac{1}{2}}=\frac{1}{2}$$ (c) $$\pi^{\log_{\pi}7}=7$$ *For (d) to (f): Use the second inverse property with base $a$: $$\log_aa^x=x$$ (d) $$\log_{11}121=\log_{11}11^2$$ - Now apply the inverse property: $$\log_{11}121=2$$ (e) $$\log_{121}11=\log_{121}\sqrt{121}=\log_{121}121^{\frac{1}{2}}$$ - Now apply the inverse property: $$\log_{121}11=\frac{1}{2}$$ (f) $$\log_3\frac{1}{9}=\log_3\frac{1}{3^2}=\log_33^{-2}$$ - Now apply the inverse property: $$\log_3\frac{1}{9}=-2$$