Question

Solve each equation below for x. (Use logarithms.)

10^(2x^(2)-5x+11) = 10000

9^(2(x-1)) = √(27)

Answer 1

just undo the operations, one by one:

10^(2x^(2)-5x+11) = 10000
take log base 10
2x^(2)-5x+11 = log10000 = 4
2x^2 - 5x + 7 = 0
(2x-7)(x+1) = 0
. . .

9^(2(x-1)) = √(27) = 3^(3/2) = 9^(3/4)
take log base 9
2(x-1) = 3/4
8x-8 = 3
8x = 11
. . .