Solve log_(x) ( log_(9) (3^(x)-9))<1

Question

Solve the inequality

x > lo g_{3} (10)

Alternative Form

x \in (lo g_{3} (10), + \infty)

Evaluate

lo g_{x} (lo g_{9} (3^{x} - 9)) < 1

Find the domain

More Steps

lo g_{x} (lo g_{9} (3^{x} - 9)) < 1, x > lo g_{3} (10)

Separate the inequality into 2 possible cases

lo g_{x} (lo g_{9} (3^{x} - 9)) < 1, x > 1 lo g_{x} (lo g_{9} (3^{x} - 9)) < 1, x < 1

Calculate

More Steps

x \in R, x > 1 lo g_{x} (lo g_{9} (3^{x} - 9)) < 1, x < 1

Calculate

More Steps

x \in R, x > 1 x \in / R, x < 1

Find the intersection

x > 1 x \in / R, x < 1

Find the intersection

x > 1 x \in / R

Find the union

x > 1

Check if the solution is in the defined range

x > 1, x > lo g_{3} (10)

Solution

x > lo g_{3} (10)

Alternative Form

x \in (lo g_{3} (10), + \infty)

Show Solution