Tính giá trị của các biểu thức sau:

a) $3^{{\log }_{3}5}$ ;                           

b) e^{ln 3};                    

c) $7^{2{\log }_{7}8}$ ;

d) $2^{lo{g}_{2}3+{\log }_{2}5}$ ;                     

e) $4^{lo{g}_2\frac{1}{5}}$ ;                   

g) 0,001^log2.

a) $3^{{\log }_{3}5}=5$ ;                                       

b) e^{ln 3} = 3;                      

c) $7^{2{\log }_{7}8}={\left[7^{lo{g}_{7}8}\right]}^2=8^2=64$ ;                        

d) $2^{lo{g}_{2}3+{\log }_{2}5}=2^{lo{g}_{2}3}{.2}^{{\log }_{2}5}=3.5=15$ ;

e) $4^{lo{g}_2\left(\frac{1}{5}\right)}={\left(2^2\right)}^{lo{g}_2\left(\frac{1}{5}\right)}$

$={\left[2^{lo{g}_2\frac{1}{5}}\right]}^2={\left[\frac{1}{5}\right]}^2=\frac{1}{25}$

g) 0,001^{log 2} = ${\left({10}^{-3}\right)}^{log2}$   = ${\left({10}^{log2}\right)}^{-3}$ = $2^{-3}$  = $\frac{1}{8}$ .