Question

Solve for x ....... thanks !

Answer 1

if we can match teh bases we can solve
because if x=x and xᵃ=xᵇ, we can conclude that a=b

16=2⁴
32=2⁵
rememeber that
`(x^m)^n=x^(mn)`


`16^(3x+2)=32^(-2x-7)`

`(2^4)^(3x+2)=(2^5)^(-2x-7)`

`2^(4(3x+2))=2^(5(-2x-7))`
2=2 so we conclude that 4(3x+2)=5(-2x-7)

4(3x+2)=5(-2x-7)
expand/distribute
12x+8=-10x-35
add 10x both sides
22x+8=-35
minus 8 both sides
22x=-43
divide both sides by 22
x=-43/22