Logarithmic inequility (lg)

[lukash]

lg⁴x - 5lg²x + 6 < 0 ???

[Math Tutor]

lg²x = t

so we have the followin inequility:

t² - 5t + 6 < 0

Can you solve it, please and I will finish the problem.

[lukash]

[tex]u_1 = 3[/tex] and [tex]u_2 = 2[/tex].
And then lg²x = 3
lg²x = 2
And here i can't continue ???

[Math Tutor]

lg²x = t
lg x = √t
lgx = √t.lg10
lgx = lg10^2√t
x = 10^√t


u1 and u2 are the solutions of the equation.
The solution of the inequility t² -5t + 6 < 0
The solution is t in (2, 3)

so x in (10^√2, 10^√3)

[Math Tutor]

If you have not understand something you can ask me questions.

[lukash]

thank you very much