Question

Вычислите:

$log_{5}0,6-log_{5}3$

$log_{2,5}25-log_{2,5}4$

$log 0,0025+log0,004$

$log_{5}0,032+log_{5}1,25$

Answer 1

log5(0.6) - log5(3) = log5(0.6/3) = log5(0.2) =log5(2/10) = log5(1/5) = log5(5^(-1)) = -1

 

log2.5(25) - log2.5(4) = log2.5(25/4) = log2.5(25*1/4) = log2.5(25*0.25) = log2.5(2.5*2.5) = 

                                       = log2.5(2.5^2) = 2

 

log(0.0025) + log(0.004) = log(0.0025*0.004) = log(0.25*10^(-2)*4*10^(-3)) = 

                                             = log(0.25*4*10^(-2)*10^(-3)) = log(1*10^(-2-3)) = log(10^(-5)) = -5

 

log5(0.032) + log5(1.25) = log5(0.032*1.25) = log5(0.04) =log5(4/100) = log5(1/25) =

                                             = log5(5^(-2)) = -2