Question

Ajuda pfv
2^x+3=2^x-3+62

Answer 1

Desenvolvendo (lembre-se das propriedades exponenciais):

$\large\begin{array}{l}\mathsf{2^{x+3}=2^{x-3}+62}\\\\\mathsf{2^{x+3}-2^{x-3}=62}\\\\\mathsf{2^x\cdot(2^3-2^{-3})=62}\\\\\mathsf{2^x\cdot(8-\dfrac{1}{8})=62}\\\\\mathsf{2^x\cdot(\dfrac{64}{8}-\dfrac{1}{8})=62}\\\\\mathsf{2^x\cdot(\dfrac{63}{8})=62}\\\\\mathsf{\dfrac{2^x\cdot63}{8}=62}\\\\\mathsf{2^x\cdot63=496}\\\\\mathsf{2^x=\dfrac{496}{63}}\end{array}$

Aplicando ㏒ de base 2 em ambos os lados da igualdade

$\large\begin{array}{l}\mathsf{\ell og_2(2^x)=\ell og_2\begin{pmatrix}\dfrac{496}{63}\end{pmatrix}}\\\\\mathsf{x\cdot\ell og_2(2)=\ell og_2\begin{pmatrix}\dfrac{496}{63}\end{pmatrix}}}\\\\\mathsf{x\cdot1=\ell og_2\begin{pmatrix}\dfrac{496}{63}\end{pmatrix}}}\\\\\fbox{ \mathsf{x=\ell og_2\begin{pmatrix}\dfrac{496}{63}\end{pmatrix}} }}\end{array}$