Question

EXERCÍCIO
11 Calcule, sem o uso da calculadora, o valor de:
a) in e
b) in 1
c) log 0,1
d) log 10​

Answer 1

a)

$ln\,e~=~x\\\\\\ln\,e~\acute{e}~o~mesmo~que~log_{_e},~logo:\\\\\\log_{_e}\,e~=~x\\\\\\e~=~e^x\\\\\\e^1~=~e^x\\\\\\\boxed{x~=~1}$

b)

$ln\,1~=~x\\\\\\log_{_e}1~=~x\\\\\\1~=~e^x\\\\\\e^0~=~e^x\\\\\\\boxed{x~=~0}$

c)

$log\,0,1~=~x\\\\\\log\,\frac{1}{10}~=~x\\\\\\log\,10^{-1}~=~x\\\\\\Lembrando,~quando~omitimos~a~base~ela~tem~valor~10\\\\\\log_{_{10}}10^{-1}~=~x\\\\\\10^{-1}~=~10^x\\\\\\\boxed{x~=~-1}$

d)

$log\,10~=~x\\\\\\log_{_{10}}10~=~x\\\\\\10~=~10^x\\\\\\10^1~=~10^x\\\\\\\boxed{x~=~1}$