9²x+¹=81x-²/3x?

Sciencemania

3 years ago

Assuming the question actually means 9^(2x+1) = [81^(x+2)]/3^x…

then you can change 9 and 81 to powers of 3…3^(2(2x+1)) = [3^(4(x+2))]/3^x

the multiply both sides by 3^x…

3^(5x+2) = 3^(4x+8)

this allows you to solve for X by setting the powers of 3 = to eachother.

5x+2 = 4x+8

then subtract 4x from the right and left

x +2 = 8

subtract 2

x=6

PS ….can be checked by putting 6 back into original equation.

Which yields 9^16 =2,541,865,828,329

=( 81^8)/(3^6) = 2,541,865,828,329 which is equal