Question

Resolver a seguinte equação exponencial:

$16^{2x+3}-16^{2x+1}=2^{8x+12}-2^{6x+5}$

Answer 1

$16^{2x+3}-16^{2x+1}=2^{8x+12}-2^{6x+5}\\\\ \dfrac{16^{2x+3}}{16^{2x+1}}= \dfrac{2^{8x+12}}{2^{6x+5}}\\\\\\ \dfrac{2^{4^{(2x+3)}}}{2^{4^{(2x+1)}}}= \dfrac{2^{8x+12}}{2^{6x+5}}\\\\\\ \dfrac{2^{8x+12}}{2^{8x+4}}= \dfrac{2^{8x+12}}{2^{6x+5}}\\\\\\8x+4=6x+5\\2x=1\\\\x= \dfrac{1}{2}$

Answer 2

Explicação passo-a-passo:

Equação exponencial !

Dada a equação :

$\mathtt{ \red{16^{2x + 3} - 16^{2x + 1} ~=~2^{8x + 12} - 2^{6x + 5} } }$

$\mathtt{ 16^{2x + 3} - 2^{8x + 12} ~=~16^{2x + 1} - 2^{6x + 5} }$

$\mathtt{ 16^{2x + 3} - 2^{(2x + 3).4}~=~(2^4)^{2x + 1} - 2^{6x + 5} }$

$\mathtt{16^{2x + 3} - (2^4)^{2x + 3}~=~ 2^{8x + 4} - 2^{6x + 5} }$

$\mathtt{\cancel{16^{2x + 3}} - \cancel{16^{2x + 3}} ~=~ 2^{8x + 4} - 2^{6x + 5} }$

$\mathtt{ 2^{8x + 4} - 2^{6x + 5}~=~0 }$

$\mathtt{\cancel{2}^{8x + 4}~=~\cancel{2}^{6x + 5} }$

$\mathtt{ 8x + 4~=~6x + 5 }$

$\mathtt{8x - 6x~=~5 - 4 }$

$\mathtt{2x~=1 }$

$\boxed{\mathtt{ \huge { \green{ x~=~ \dfrac{1}{2} } } } }$

Espero ter ajudado bastante!)