Question

29. Dados log 2 = 0,30; log 3 = 0,48; log 5 = 0,70 e log e = 0,43, resolva as equações:

a) 2* = 5;s = (2,33}

b) e* = 3;5 = {1,12}

c) 5* = e;s = (0,61}

d) e* - 6 = 0. S (1,81}

me ajudem por favor :'3​

Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf 2^x=5\\\sf x=\ell og_25\\\sf x=\dfrac{\ell og5}{\ell og2}\\\sf x=\dfrac{0,7}{0,3}\\\sf x=2,33...\\\tt b)~\sf e^x=3\\\sf x=\ell og_e3\\\sf x=\dfrac{\ell og3}{\ell oge}\\\sf x=\dfrac{0,48}{0,43}\\\sf x=1,12\\\tt c)~\sf 5^x=e\\\sf x=\ell og_5e\\\sf x=\dfrac{\ell oge}{\ell og_5}\\\sf x=\dfrac{0,43}{0,70}\\\sf x=0,61\end{array}}$

$\large\boxed{\begin{array}{l}\sf\tt d)~\sf e^x-6=0\\\sf e^x=6\\\sf x=\ell og_e6\\\sf x=\dfrac{\ell og6}{\ell oge}\\\sf x=\dfrac{\ell og3+\ell og2}{\ell oge}\\\sf x=\dfrac{0,48+0,30}{0,43}\\\sf x=\dfrac{0,78}{0,43}\\\sf x=1,81\end{array}}$