Question

Sendo log2 = 0,3, log3 = 0,4 e log5 = 0,7, o $log_{2}50$ é:

$a) \: \frac{17}{3} \\ \\ b) \: \frac{15}{4} \\ \\ c) \: \frac{3}{8} \\ \\ d) \: 3$
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Answer 1

$log2=0,3\\log3=0,4\\log5=0,7\\\\\boxed{log_ab=\dfrac{loga}{logb}}\\\\log_250=\dfrac{log50}{log2}\\\\log_250=\dfrac{log(2\cdot5\cdot5)}{log2}\\\\\boxed{log_a(b\cdot c)=log_ab+log_ac}\\\\log_250=\dfrac{log2+log5+log5}{log2}\\\\log_250=\dfrac{0,3+0,7+0,7}{0,3}\\\\log_250=\dfrac{1,7}{0,3}=\dfrac{17}{3}\\\\Alternativa\;(a)\;\dfrac{17}{3}$