Question

Dado que log 2 = 0,3 e log 3 = 0,5 , determine:
a) log256
b) log36
c) log (1/9)
d) log 0,12

Answer 1

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$\tt a)~\sf\ell og256=\ell og2^8=8\cdot\ell og2\\\sf =8\cdot0,3=2,4\checkmark\\\tt b)~\sf\ell og36=\ell og(2^2\cdot3^2)=\ell og2^2+\ell og3^2\\\sf =2\ell og2+2\ell og3=2\cdot0,3+2\cdot0,5\\\sf =0,6+1=1,6\checkmark\\\tt c)~\sf\ell og\left(\dfrac{1}{9}\right)=\ell og1-\ell og9\\\sf =\ell og1-\ell og3^2=\ell og1-2\ell og3\\\sf =0-2\cdot0,5=-1\checkmark\\\tt d)~\sf\ell og0,12=\ell og\left(\dfrac{12}{100}\right)=\ell og12-\ell og100\\\sf= \ell og(2^2\cdot3)-\ell og 10^2=\ell og2^2+\ell og3-2\ell og10$

$\sf 2\ell og2+\ell og3-2\ell og10=2\cdot0,3+0,5-2\cdot1\\\sf =0,6+0,5-2=-0,9\checkmark$