# Solve 9^a - 10 * 3^a + 9 = 0

can someone please offer assistance?

Go to main content# Solve 9^a - 10 * 3^a + 9 = 0

can someone please offer assistance?

Sure.

or, 9^{a} - 10 × 3^{a} + 9 = 0

or, 3^{2a} - 10 × 3^{a} + 9 = 0

let 3^{a} = k

or, k^{2} - 10.k + 9 = 0

or, k^{2} - (9 + 1)k + 9 = 0

or, k^{2} - 9k - k + 9 = 0

or, k(k - 9) - 1(k - 9) = 0

or, (k - 9)(k - 1) = 0

Either, k = 9

so, 3^{a} = 3^{2}

so, a = 2

OR, k = 1

so, 3^{a} = 3^{0}

so, a = 0

∴ a = 0, 2

Video explanation: