Question

how would i solve \[9^{2x+1}=81(27^x)\]

Answer 1

convert all to base 3
hence we have 3^2(2x+1)=(3^4)(3^(3x))
on multiplication since power gets added
we have3^(4x+2)=3^(4+3x)
thus 4x+2=4+3x
or 4x-3x=4-2
or x=2

Answer 2

so this would apply to all equations with numbers that have a common multiple then ?

Answer 3

i would have to convert all the base with the common multiple right?

Answer 4

ok thanks!