Question

Sendo log 2 = 0,3; log3 = 0,4 e log5 = 0,7, calcule:a) log 50  na base 2         b) log 45 na base 3c) log 2 na base 9            d) log 600 na base 8f) log 15 na base 6

Answer 1

a) $log_{2} 50 = \frac{log50}{log2} = \frac{log(5*2*5)}{log2} = \frac{log5 + log2 + log5}{0,3} = \frac{0,7+0,3+0,7}{0,3} = \frac{1,7}{0,3} = 5$

b) $log_3 45 = \frac{log45}{log3} = \frac{log(3^2*5)}{log3} = \frac{log3^2 + log5}{0,4} = \frac{2log3 + 0,7}{0,4} \\ \frac{2*0,4+0,7}{0,4} = \frac{1,5}{0,4} = 3,75$

c) $log_92 = \frac{log2}{log9} = \frac{0,3}{log3^2} = \frac{0,3}{2log3} = \frac{0,3}{2*0,4} = \frac{0,3}{0,8} = 0,375$

d) $log_8600 = \frac{log2^3}{log(100*2*3)} = \frac{3log2}{log100 + log2 + log3} = \frac{3*0,3}{2+0,3+0,4} = \frac{0,9}{2,7} = 0,33$

e)  $log_6 15 = \frac{log15}{log6} = \frac{log(3*5)}{log(3*2)} = \frac{log3 + log5}{log3 + log2} = \frac{0,4+0,7}{0,4+0,3} = \frac{1,1}{0,7} = 1,55$