Question

1) Se log m=2 e log n= 3, então log√mn é igual a?

2) o valor da expressão log5 125 + log2 32 é?

Answer 1

1)

$log_{10}\;\sqrt{m.n}\\ \\log_{10}\;\left(m.n\right)^{\frac{1}{2}}\\\\\frac{1}{2} \left(log_{10}\;m.n\right)\\\\\frac{1}{2} \left(log_{10}\,m+log_{10}\,n\right)\\\\\frac{1}{2} \left(2+3\,n\right)\\\\\frac{1}{2} .5\\\\\frac{5}{2}$

2)

$log_5\,125=x\\\\125=5^x\\\\5^3=5^x\\\\x=3\\\\\\log_2\,32=y\\\\2^5=2^y\\\\y=5$

Assim:

log5 125 + log2 32 = x + y = 3 + 5 = 8