a)log(3)81=log(3)3⁴=4log(3)3=4•1=4
b)log(5)✓125=log(5)✓5³=
[tex] = log_{5}(5 {}^{ \frac{3}{2} } ) = \frac{3}{2} log_{5}(5) = \\ = \frac{3}{2} \times 1 = \frac{3}{2} [/tex]
c)
[tex] log_{2}( \frac{1}{ \sqrt[6]{128} } ) = log_{2}( \frac{1}{ \sqrt[6]{ {2}^{7} }} ) = \\ = log_{2}( \frac{1}{ {2}^{ \frac{7}{6} } } ) = log_{2}( {2}^{ - \frac{7}{6} } ) = - \frac{7}{6} log_{2}(2) = \\ = - \frac{7}{6} \times 1 = - \frac{7}{6} [/tex]
d)lg 1/✓100= log1/10= lg 10^-1=
= -1lg10= -1•1=-1
e)ln 1/✓⁴✓e = ln 1/⁸✓e==ln 1/e ^ 1/8=
=ln e ^-1/8 = -1/8 ln e = -1/8 •1 = -1/8
