Question

Sabendo que log2=0,30, log3=0,47, log22=1,34 e calcule:
a) Log12=
b) Log18=
c) Log5=
d) Log11=
e) Log44=

Answer 1

Explicação passo-a-passo:

●Logaritmos

↘Para solucionar o problema em questão é necessário ter em mente as seguintes propriedades.

$\red {\boxed {\mathbf {log^{a*b}~=~log^a~+log^b}}}$

$\red {\boxed {\mathbf {log^{\frac {a}{b}}~=~log^a~-log^b}}}$

■Resolução

a)

$\sf {log^{12}}$

$\iff\sf {log^{3*2^2}}$

$\iff\sf {log^{3}+log^{2^2}}$

$\iff\sf {0,47+2*0,3}$

$\iff\sf {0,47+0,6}$

$\iff\sf {\red {1,07}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

b)

$\sf {log^{18}}$

$\iff\sf {log^{3^2*2}}$

$\iff\sf {log^{3^2}+log^{2}}$

$\iff\sf {2*log^3+log^{2}}$

$\iff\sf {2*0,47+0,3}$

$\iff\sf {0,94+0,3}$

$\iff\sf {\red {1,24}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

c)

$\sf {log^5}$

$\iff\sf {log^{\frac {10}{2}}}$

$\iff\sf {log^{10}~-~log^2}$

$\iff\sf {1~-~0,3}$

$\iff\sf {\red {0,7}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

d)

$\sf {log^{11}}$

$\iff\sf {log^{\frac {22}{2}}}$

$\iff\sf {log^{22}~-~log^2}$

$\iff\sf {1,34~-~0,3}$

$\iff\sf {\red {1,04}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

e)

$\sf {log^{44}}$

$\iff\sf {log^{22*2}}$

$\iff\sf {log^{22}+log^{2}}$

$\iff\sf {1,34+0,3}$

$\iff\sf {\red {1,64}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

⇒Espero ter ajudado! :)

⇒ Att: Jovial Massingue