Question

I need help with this

Answer 1

`{ 3 }^( - 1) * {3}^(x + 1) - { 3}^(x - 2) + {3}^( - 2) * { 3}^(x + 3) = 35 \\ {3}^( - 1 + x + 1) - {3}^(x - 2) + {3}^( - 2 + x + 3) = 35 \\ {3}^(x) - {3}^(x - 2) + { 3}^( - 2 + 3 + x) = 35 \\ { 3 }^(x) - {3}^(x - 2) + {3}^(x + 1) = 35 \\ {3}^(x) - {3}^(x) * {3}^( - 2) + {3}^(x) * {3}^(1) = 35 \\ {3}^(x) (1 - {3}^( - 2) + 3) = 35 \\ {3}^(x) (3 + 1 - (1)/(9)) = 35 \\ \\ {3}^(x) (4 - (1)/(9) ) = 35 \\ {3}^(x) ( (35)/(9) ) = 35 \\ \frac{ {3}^(x)( (35)/( 9 ) )}{ (35)/(9) } = 35 / ( (35)/(9) ) \\ {3}^(x) = 9 \\ {3}^(x) = { 3 }^(2) \\ x = 2`

ATTACHED IS THE SOLUTION.

I USED THE LAWS OF EXPONENTS.

GOODLUCK.