How do you solve these logarithm-related questions

Question 1:

p = log ( base 9 ) x, find log ( base 3x ) 81 in terms of p.

Question 2:

2 log( base 10 )x^2y = 3 + log (base 10 ) y where x and y are both positive, express y in terms of x. If x-2y =1, find the value of x and y.

1)
p = log_9(x)
x = 9^p
let log_3x(81) = u , then:
(3x)^u = 81
(3 * 9^p)^u = 81
[3^(2p + 1)]^u = 81
3^[u(2p + 1)] = 3^4
u(2p + 1) = 4
u = 4/(2p + 1)

2)
log(x^2y) = 3 + log(y)
x - 2y = 1 => x = 2y + 1
log[y(2y + 1)^2] - log(y) = 3
log[y(2y + 1)^2 / y] = 3
4y^2 + 4y + 1 = 10^3 = 1000
y^2 + y = 999/4
y^2 + y + (1/2)^2 = 999/4 + 1/4
(y + 1/2)^2 = 250
y + 1/2 = ±√250
y = - 1/2 ± 5√10
x = -1 ± 10√10 + 1
x = ± 10√10

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