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Popular >

5^{2x+1}>5^x+4

Solution

5^{2 x + 1} > 5^{x} + 4

Solution

x > 0

+1

Interval Notation

(0, \infty)

Solution steps

5^{2 x + 1} > 5^{x} + 4

Apply exponent rules

(5^{x})^{2} \cdot 5 > 5^{x} + 4

Let

u = 5^{x}

u^{2} \cdot 5 > u + 4

u^{2} \cdot 5 > u + 4 : u < - \frac{4}{5} or u > 1

u < - \frac{4}{5} or u > 1

Substitute back

u = 5^{x}

5^{x} < - \frac{4}{5} or 5^{x} > 1

5^{x} < - \frac{4}{5} :

No Solution

5^{x} > 1 : x > 0

Combine the intervals

No Solution or x > 0

Merge Overlapping Intervals

x > 0

Popular Examples

3e^x-5e^{-x}-2>0

3 e^{x} - 5 e^{- x} - 2 > 0

6^{x} > \frac{1}{36}

2^{1 - x^{2}} < 8

3^{x} < 5

2^{x} > 6

Frequently Asked Questions (FAQ)

What is 5^{2x+1}>5^x+4 ?
The solution to 5^{2x+1}>5^x+4 is x>0