Question

determine a seguinte equação exponencial

7^x-1 +7 ^x+1 = 50

Answer 1

$7 ^{x-1} +7 ^{x+1} = 50 \\ \\ 7 ^{x} .7 ^{-1}+7 ^{x}.7 ^{1}=50 \\ \\ 7 ^{x}(7 ^{-1}+7 ^{1})=50 \\ \\ 7 ^{x}( \frac{1}{7} +7)=50 \\ \\ 7 ^{x}( \frac{50}{7} )=50 \\ \\ 7 ^{x}= \frac{50}{ \frac{50}{7} } \\ \\ 7 ^{x}=50. \frac{7}{50} \\ \\ 7 ^{x-1} +7 ^{x+1} = 50 \\ \\ 7 ^{x} .7 ^{-1}+7 ^{x}.7 ^{1}=50 \\ \\ 7 ^{x}(7 ^{-1}+7 ^{1})=50 \\ \\ 7 ^{x}( \frac{1}{7} +7)=50 \\ \\ 7 ^{x}( \frac{50}{7} )=50 \\ \\ 7 ^{x}= \frac{50}{ \frac{50}{7} } \\ \\ 7 ^{x}=7 x=1$