Verified answer

Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\sf \left(\dfrac{1}{3}\right)^x = 27[/tex]

[tex]\sf 3^{-x} = 3^3[/tex]

[tex]\boxed{\boxed{\sf x = -3}}[/tex]

[tex]\sf 5^{2x - 7} = 125[/tex]

[tex]\sf 5^{2x - 7} = 5^3[/tex]

[tex]\sf 2x - 7 =3[/tex]

[tex]\sf 2x = 10[/tex]

[tex]\boxed{\boxed{\sf x = 5}}[/tex]

[tex]\sf log\:10x - log\:(4 - x) = 2[/tex]

[tex]\sf log\left(\dfrac{10x}{4 - x}\right) = 2[/tex]

[tex]\sf log\left(\dfrac{10x}{4 - x}\right) = log\:100[/tex]

[tex]\sf \dfrac{10x}{4 - x} = 100[/tex]

[tex]\sf 10x = 400 - 100x[/tex]

[tex]\sf 110x = 400[/tex]

[tex]\boxed{\boxed{\sf x = \dfrac{40}{11}}}[/tex]

[tex]\sf ln\:(x + 1) + ln(x - 2) = 1[/tex]

[tex]\sf ln\:(x + 1)\:.\:(x - 2) = ln\:e[/tex]

[tex]\sf x^2 - x - 2 = e[/tex]

[tex]\sf x^2 - x - 2 - e = 0[/tex]

[tex]\sf \Delta = b^2 - 4.a.c[/tex]

[tex]\sf \Delta = (-1)^2 - 4.1.(-2-e)[/tex]

[tex]\sf \Delta = 1 + 8 + 4e[/tex]

[tex]\sf \Delta = 9 + 4e[/tex]

[tex]\sf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{9 + 4e}}{2} \rightarrow \begin{cases}\sf{x' = \dfrac{1 + \sqrt{9 + 4e}}{2}}\\\\\sf{x'' = \dfrac{1 \pm \sqrt{9 - 4e}}{2}}\end{cases}}[/tex]

[tex]\boxed{\boxed{\sf S = \left\{\:\dfrac{1 + \sqrt{9 + 4e}}{2}\:\right\}}}[/tex]