• Equações Exponenciais.

• DEFINIÇÃO:

É uma expressão algébrica com uma igualdade, cuja qual, contém uma incógnita em seu expoente. Base + (positiva) e ≠ 1 não igual a 1.

• RESOLUÇÃO:

1)

[tex]\sf7^{x}=\sqrt[3]{49}\\\\\sf\sqrt[3]{49}\Rightarrow\sqrt[3]{7^2}\Rightarrow\boxed{\sf\sqrt[n]{a^m}=a^{\frac{m}{n}}}\bigstar~\Rightarrow~7^{\frac{2}{3}}~\checkmark\\\\\backslash\!\!\!7^x=\backslash\!\!\!7^{\frac{2}{3}}\\\\\boxed{\sf\bold{x=\frac{2}{3}}}~\checkmark[/tex]

2)

[tex]\sf9^x=\frac{1}{27}\\\\\sf9^x\Rightarrow\left(3^2\right)^x\Rightarrow3^{2x}~\checkmark\\\\\sf\frac{1}{27}\Rightarrow\frac{1}{3^3}\Rightarrow\boxed{\sf\frac{1}{a^n}=a^{-n}}\bigstar~\Rightarrow3^{-3}~\checkmark\\\\\sf\backslash\!\!\!3^{2x}=\backslash\!\!\!3^{-3}\Rightarrow2x=-3\Rightarrow\boxed{\bold{\sf~x-\frac{3}{2}}}~\checkmark[/tex]

3)

[tex]\sf3^x=\sqrt{27}\\\\\sf\sqrt{27}\Rightarrow\sqrt{3^3}\Rightarrow\boxed{\sqrt[n]{a^m}=a^{\frac{m}{n}}}\bigstar\Rightarrow3^{\frac{3}{2}}\\\\\sf\backslash\!\!\!3^x=\backslash\!\!\!3^{\frac{3}{2}}\Rightarrow\boxed{\sf~x=\frac{3}{2}}~\checkmark[/tex]

4)

[tex]\sf8^x=\sqrt{32}\\\\\sf8^x\Rightarrow\left(2^3\right)^x\Rightarrow2^{3x}~\checkmark\\\\\sf\sqrt{32}\Rightarrow\sqrt{2^5}\Rightarrow\boxed{\sf\sqrt[n]{a^m}=a^{\frac{m}{n}}}\bigstar\Rightarrow2^{\frac{5}{2}}\\\\\sf\backslash\!\!\!2^{3x}=\backslash\!\!\!2^{\frac{5}{2}}\Rightarrow3x=\frac{5}{2}\Rightarrow~x=\frac{\frac{5}{2}}{3}\Rightarrow\frac{5}{2}\cdot\frac{1}{3}\Rightarrow~x=\frac{5\cdot1}{2\cdot3}\Rightarrow~\boxed{\sf~x=\frac{5}{6}}~\checkmark[/tex]

✨ [tex]\Large\mathscr{\blue{Per:~Dan}}[/tex] ✨