logarithms?

Question

How can one answer this one? Please explain. Thank you!
(log7x)^2 – 3log7x = -2

*the number 7 above is the base

Answer 1

log7x = t
you have a quadratic equation
t^2 -3t +2 = 0
when you solve it you get
t = 1 or t = 2
x = 7^1 = 7
or x = 7^2 = 49

Answer 2

for simplicity of reading, everywhere i say log x i mean log x to the base 7

(logx)^2 - 3logx +2 = 0
(logx - 2)(logx -1) = 0
log x = 2 => x = 7^2 = 49
or log x = 1 => x = 7

so x = 7 or x = 49

Answer 3

Let log mean log base 7 in the following:-
log x² - 3 log x = - 2
log x² + log x^(-3) = - 2
log (1 / x) = - 2
(1/x) = 7^(-2) = 1 / 49
x = 49

Answer 4

let y = log 7x
y^2 - 3 x + 2 = 0
(y -2) (y - 1) = 0
y = 2 . . . and . . . y = 1
or
log 7x = 1
7x =10
x = 10 / 7 . . . . one answer

log 7x = 2
10^2 = 7x
7x = 100
x = 100 / 7 . . . . another answer