Question

dados log de 2 = 0,30 e log de 3 = 0,45 e log de 5 = 0,70 calcule log de 20 + log de 18​

Answer 1

Temos

$\log2=0,30\\\log3=0,45\\\log5=0,70$

E queremos $\log20+\log18$

usando as seguintes propriedade

• $\log a^b=b\cdot\log a$

• $\log(a\cdot b)=\log a+\log b$

$\log20+\log18\\\\\log4\cdot5+\log2\cdot9\\\\\log4+\log5+\log2+\log9\\\\\log2^2+\log5+\log2+\log3^2\\\\2\overbrace{\log2}^{0,30}+\overbrace{\log 5}^{0,70}+\overbrace{\log2}^{0,30}+2\cdot\overbrace{\log3}^{0,45}\\\\2\cdot0,30+0,70+0,30+0,9\\\\0,6+0,70+0,30+0,9=2,5$

Então $\boxed{\boxed{\log20+\log18=2,5}}$