Question

Considere os números reais:

A=log 15⁴¹ B=log 17⁴°
15 17

C=log 17^80 D=log 15¹³²
17² 15³

Coloque-os em ordem crescente. ajudaaaa

Answer 1

$\mathrm{A=\log_{15}{15^{41}}=41\log_{15}{15}=41.1\ \to\ A=41}\\\\ \mathrm{B=\log_{17}{17^{40}}=40\log_{17}{17}=40.1\ \to\ B=40}\\\\ \mathrm{C=\log_{17^2}{17^{80}}=\dfrac{80}{2}\log_{17}{17}=40.1\ \to\ C=40}\\\\ \mathrm{D=\log_{15^3}{15^{132}}=\dfrac{132}{3}\log_{15}{15}=44.1\ \to\ D=44}\\\\ \mathbf{Ordem\ crescente:\{40,40,41,44\}=\{B,C,A,D\}}$