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