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Popular >

9^x+3^x-6>0

Solution

9^{x} + 3^{x} - 6 > 0

Solution

x > lo g_{3} (2)

+2

Interval Notation

(lo g_{3} (2), \infty)

Decimal Notation

x > 0.63092 \dots

Solution steps

9^{x} + 3^{x} - 6 > 0

Apply exponent rules

(3^{x})^{2} + 3^{x} - 6 > 0

Let

u = 3^{x}

u^{2} + u - 6 > 0

u^{2} + u - 6 > 0 : u < - 3 or u > 2

u < - 3 or u > 2

Substitute back

u = 3^{x}

3^{x} < - 3 or 3^{x} > 2

3^{x} < - 3 :

No Solution

3^{x} > 2 : x > lo g_{3} (2)

Combine the intervals

No Solution or x > lo g_{3} (2)

Merge Overlapping Intervals

x > lo g_{3} (2)

Popular Examples

(5^x+625)/((5^x-130))<= 0

\frac{5 ^{x} + 625}{( 5 ^{x} - 130 )} \leq 0

(1/3)^{sqrt(x+2)}>3^{-x}

(\frac{1}{3})^{x + 2} > 3^{- x}

(3^{x})^{2} < 1 5^{x}

2 7^{x} < 9^{x^{2} - 1}

4^x-2*2^x-8<= 0

4^{x} - 2 \cdot 2^{x} - 8 \leq 0

Frequently Asked Questions (FAQ)

What is 9^x+3^x-6>0 ?
The solution to 9^x+3^x-6>0 is x>log_{3}(2)