Respuesta:
a) Log (15) + log (2) - log (5)
[tex]=log (5) + log (\frac{2}{5})[/tex]
[tex]=log (15*\frac{2}{5} )[/tex]
[tex]=log (6)[/tex]
b) 3·log(2) + 2·log(3)
[tex]=log (2^{3} ) + log (3^{2} )[/tex]
[tex]=log (8) + log (9)[/tex]
[tex]=log (8*9)[/tex]
[tex]=log (72)[/tex]
c)2·log(3)+4·log(2)−2·log(12)
[tex]=log (3^{2} ) + log (2^{4}) - log (12^{2} )[/tex]
[tex]=log (3^{2} ) + log (\frac{2^{4} }{12^{2} } )[/tex]
[tex]=log (\frac{2^{4} }{3^{2} *2^{4} } )[/tex]
[tex]=log (\frac{3^{2} *2^{4} }{3^{2}* 2^{4} })[/tex]
[tex]=log (1) \\=0[/tex]
d) log3(45)−log3(5)
[tex]=log_{3} (\frac{45}{5} )[/tex]
[tex]=log_{3} (9)\\ \\= log_{3} (3^{2} )\\= 2[/tex]
e) log5(10)+log5(1/2)
[tex]=log_{5} (10*\frac{1}{2} )\\=log _{5} (5)\\=1[/tex]
f) 2log(1000)+4⋅log(10)−3log(1000)
[tex]=2 log (10^{3} ) + 4 log (10) - 3 log ( 10^{3} )[/tex]
[tex]=3*2 log (10) + 4 log (10) - 3*3 log (10)[/tex]
[tex]=6 log (10) + 4 log (10) - 9 log (10)\\=log (10)\\=1[/tex]
El asterisco utilizado, es para representar que se está multiplicando.
