Question

1 - Determine o valor de cada expressão, considerando log 2= 0,3 ; log 5 =0,7 ; log 7 = 0,8

a) $log_{5}$28

b) $log_{7}$14

c) $log_{14}$70

Answer 1

a) log$log_{5}28= \frac{log28}{log5}= \frac{log4.7}{log5}= \frac{log4+log7}{log5}= \frac{log 2^{2}+log7 }{log5} = \frac{2.0,3+0,8}{0,7} = \frac{0,6+0,8}{0,7} =$
$\frac{1,4}{0,7} = 2$

b) $log_{7}14= \frac{log14}{log7}= \frac{log2.7}{log7}= \frac{log2+log7}{log7}= \frac{0,3+0,8}{0,8} = \frac{1,1}{0,8} = \frac{11}{8}$

c) $log_{14}70= \frac{log70}{log14}= \frac{log10.7}{log2.7}= \frac{log10+log7}{log2+log7}= \frac{1+0,8}{0,3+0,8}= \frac{1,8}{1,1}= \frac{18}{11}$