Question

Dado LOGa=5 ,Log B-2 e log c -1 calcule
log(√a.c)
log abc
log a².b³
       $c^{4}$

Answer 1

Olá, Ingridsirino.

$\log a=5 ,\log b=2,\log c =1\\\\ \log(\sqrt {a\cdot c})=\log (a\cdot c)^{\frac12}=\frac12\log(a\cdot c)=\frac12(\log a+\log c)=\frac12\cdot(5+1)=\\=\frac12\cdot6=3\\\\ \log(abc)=\log a+\log b+\log c=5+2+1=8\\\\ \log \frac{a\²\cdot b\³}{c^{4}}=\log(a\²\cdot b\³)-\log{c^{4}}=\log a^2+\log b^3-\log c^4=\\\\ =2\log a+3\log b-4\log c=2\cdot5+3\cdot2-4\cdot1=10+6-4=12$