tex]...

September 2021 2 7 Report

Вычислите:

[tex]log_{5}0,6-log_{5}3[/tex]

[tex]log_{2,5}25-log_{2,5}4[/tex]

[tex]log 0,0025+log0,004[/tex]

[tex]log_{5}0,032+log_{5}1,25[/tex]

dtnth

$log_5 0.6-log_5 3=log_5 \frac{0.6}{3}=log_5 \frac{1}{5}=log_5 5^{-1}=-1$

$log_{2.5} 25-log_{2.5} 4=log_{2.5} \frac{25}{4}=log_{2.5} 6.25=log_{2.5} 2.5^2=2$

$lg 0.0025+lg 0.004=lg (0.025*0.004)=lg 0.000 1=log_{10} 10^{-4}=-4$

$log_5 0.032+log_5 1.25=log_5 0.032*1.25=log_5 0.04=log_5 5^{-2}=-2$

5 votes Thanks 10

BerezinaEV

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

3 votes Thanks 7