LOGaritma
sifat
Penjelasan dengan langkah-langkah:
[tex]\sf a). ^2log {\frac{1}{64}}+ ^2log3 + ^9log 16 - ^{\frac{1}{9}}log 3[/tex]
[tex]\sf =^2log2^{-6}+ ^2log3 + ^{3^2}log 2^4 - ^{3^{-2}}log 3[/tex]
[tex]\sf = -6. ^2log 2 + ^2log3 + \frac{4}{2}^3log 2 - (-\frac{1}{2})^3log 3[/tex]
[tex]\sf = -6(1) + ^2log3 + 2 ( ^3log 2) - (-\frac{1}{2})(1)[/tex]
[tex]\sf = -6 + ^2log3 + 2 .\ ( ^3log 2) +\frac{1}{2}[/tex]
[tex]\sf = ^2log3 + 2 .\ ^3log 2 - 5\frac{1}{2}\\\\[/tex]
[tex]\sf b). Tentukan \ nilai \ x \ dari \sqrt[\sf 3x+1]{7} = \sqrt[\sf x-2]{3}[/tex]
[tex]\sf 7^{\frac{1}{3x+1}} =3^{\frac{1}{x-2}}[/tex]
[tex]\sf \log (7^{\frac{1}{3x+1}}) =\log (3^{\frac{1}{x-2}})[/tex]
[tex]\sf \dfrac{\log7}{3x+1} = \dfrac{\log3}{x-2}[/tex]
(x- 2) log 7 = (3x +1) log 3
x log 7 - 2 log 7 = 3x log 3 + log 3
x log 7 - 3x log 3 = log 3 + 2log 7
x (log 7 - 3 log 3) = log 3 + 2 log 7
[tex]\sf x = \dfrac{\log\ 3+ 2. \log \ 7}{\log \ 7 - 3 \log \ 3}[/tex]
[tex]\sf x = \dfrac{\log\ 3+ \log \ 7^2}{\log \ 7 - \log \ 3^3}[/tex]
[tex]\sf x = \dfrac{\log\ 3+ \log \ 49}{\log \ 7 - \log \ 27}[/tex]
