Question

log 27=x base√3
por favor me ajudem !!!❤❤❤

Answer 1

$\large\textsf{Principais propriedades exponenciais:}\\\\\\\mathsf{P1.~~a^m\cdot a^n=a^{m+n}}\\\\\\\mathsf{P2.~~\dfrac{a^m}{a^n}=a^{m-n}~~~~(para~a \neq0~e~m \geq n)}\\\\\\\mathsf{P3.~~(a\cdot b)^n=a^n\cdot b^n}\\\\\\\mathsf{P4.~~(\dfrac{a}{b})^n=\dfrac{a^n}{b^n}~~~~(b \neq 0)}\\\\\\\mathsf{P5.~~(a^m)^n=a^{m\cdot n}}\\\\\\\textsf{Expoente racional:}~~\large\fbox{ \mathsf{a^{\frac{b}{c}}=\sqrt[c]{\mathsf{a^b}}} }\\\\\\\textsf{Expoente inteiro negativo:}~~\fbox{ \mathsf{a^{-n}=\dfrac{1}{a^n}} }$


$\large\textsf{Principais propriedades dos logaritmos:}\\\\\\\mathsf{P1.~~\ell og_a(b\cdot c)=\ell og_a b+\ell og_a c}\\\\\\\mathsf{P2.~~\ell og_a(\dfrac{b}{c})=\ell og_ab-\ell og_ac}\\\\\\\mathsf{P3.~~\ell og_ab^{\alpha}=\alpha\cdot\ell og_ab}\\\\\\\textsf{Mudan\c{c}a~de~base:}~~\fbox{ \mathsf{\ell og_ab=\dfrac{\ell og_ca}{\ell og_cb}} }$


$\large\textsf{Ap\'os esse breve resumo, vamos atacar a quest\~ao:}$


$\large\begin{array}{l}\mathsf{\ell og_{\sqrt{3}}~27=x}\\\\\\{\begin{pmatrix}\mathsf{\sqrt{3}}\end{pmatrix}\mathsf{^x=27}\\\\\\\mathsf{(3^{\frac{1}{2}})^x=27}\\\\\\\mathsf{3^{\frac{x}{2}}=27}\\\\\\\mathsf{3^{ \frac{x}{2} }=3^3~~~~(igualando~os~expoentes)}\\\\\\\mathsf{\dfrac{x}{2}=3}\\\\\\\mathsf{x=2\cdot 3}\\\\\\\Large\fbox{ \mathsf{x=6} }\end{array}$