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Popular >

3^{2x+3}+3^{x+1}-4>0

Solution

3^{2 x + 3} + 3^{x + 1} - 4 > 0

Solution

x > - 1

+1

Interval Notation

(- 1, \infty)

Solution steps

3^{2 x + 3} + 3^{x + 1} - 4 > 0

Apply exponent rules

(3^{x})^{2} \cdot 3^{3} + 3^{x} \cdot 3 - 4 > 0

Let

u = 3^{x}

u^{2} \cdot 3^{3} + u \cdot 3 - 4 > 0

u^{2} \cdot 3^{3} + u \cdot 3 - 4 > 0 : u < - \frac{4}{9} or u > \frac{1}{3}

u < - \frac{4}{9} or u > \frac{1}{3}

Substitute back

u = 3^{x}

3^{x} < - \frac{4}{9} or 3^{x} > \frac{1}{3}

3^{x} < - \frac{4}{9} :

No Solution

3^{x} > \frac{1}{3} : x > - 1

Combine the intervals

No Solution or x > - 1

Merge Overlapping Intervals

x > - 1

Popular Examples

2^{n} - 1 > 1000000

9^{x} + 3^{x} - 2 < 0

(2^n)/(2^n+2-3)< 1/4

\frac{2 ^{n}}{2 ^{n} + 2 - 3} < \frac{1}{4}

4^{1+x}+4^x>= 5

4^{1 + x} + 4^{x} \geq 5

e^{x} \geq 2

Frequently Asked Questions (FAQ)

What is 3^{2x+3}+3^{x+1}-4>0 ?
The solution to 3^{2x+3}+3^{x+1}-4>0 is x>-1