Question

Não estou entendendo está equação de função exponencial e logaritmo

2^x-3 + 2^x-4 = 2^x-2 -2^x-1 +14

Resposta = 5

Answer 1

$2^{x-3}+2^{x-4}=2^{x-2}-2^{x-1}+14\\\\ 2^x *2^{-3} + 2^{x}*2^{-4}=2^{x}*2^{-2}-2^{x}*2^{-1}+14\\\\2^x*(2^{-3}+2^{-4})=2^x*(2^{-2}-2^{-1})+14 \\\\ 2^x*(2^{-3}+2^{-4}) - 2^x*(2^{-2}-2^{-1})=14\\\\2^{x}*(2^{-3}+2^{-4}-2^{-2}+2^{-1})=14\\\\ 2^{x}* (\frac{1}{2^3} +\frac{1}{2^4} -\frac{1}{2^2}+\frac{1}{2})=14 \\\\2^{x}*( \frac{7}{16})=14\\\\2^x= 14*\frac{16}{7} \\\\2^{x}= 2*16\\\\2^x=2*2^4\\\\2^x = 2^5\\x=5$