Question

sabendo q log^2 =a e log^3=b, calcule em função de a e b a) log 6 b) log 1,5 c) log 5 d) log 30 e) log 1/4

Answer 1

Se $log 2=a$  e  $log3=b$ .

a)
$log 6 = log{2.3}=log2+log3=a+b$

b)
$log1,5=log{\frac{3}{2}}=log3 - log2=b-a$

c)
$log5=log{\frac{10}{2}}=log10-log2=1-a$

d)
$log30=log{3.10}=log3 + log10=b+1$

e)
$log{\frac{1}{4}=log1-log4=log1-log2^2=log1-2log2=0-2a=-2a$

f)
$log72=log8.9=log 8 + log 9=log2^3+log3^2=\\ =3.log2+2log3=3a+2b$

g)
$log0,3=log{\frac{3}{10}}=log3-log10=b-1$

i)
$log0,024=log{\frac{24}{1000}}=log{\frac{8.3}{1000}}=\\ =log8 + log3 -log1000 = log2^3+log3-log10^3=\\ =3log2+log3-3log10=3a+b+3$

j)
$log0,75=log{\frac{3}{4}}=log3 - log4=log3-log2^2=\\ =log3-2log2=b-2a$