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Popular >

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

Solution

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

Solution

x > ln (\frac{5}{3})

+2

Interval Notation

(ln (\frac{5}{3}), \infty)

Decimal Notation

x > 0.51082 \dots

Solution steps

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

Apply exponent rules

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

Let

u = e^{x}

3 u^{2} - 5 - 2 u > 0

3 u^{2} - 5 - 2 u > 0 : u < - 1 or u > \frac{5}{3}

u < - 1 or u > \frac{5}{3}

Substitute back

u = e^{x}

e^{x} < - 1 or e^{x} > \frac{5}{3}

e^{x} < - 1 :

No Solution

e^{x} > \frac{5}{3} : x > ln (\frac{5}{3})

Combine the intervals

No Solution or x > ln (\frac{5}{3})

Merge Overlapping Intervals

x > ln (\frac{5}{3})

Popular Examples

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

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

3^{x} < 5

2^{x} > 6

(4^{x})^{2} - 4 < 0

Frequently Asked Questions (FAQ)

What is 3e^x-5e^{-x}-2>0 ?
The solution to 3e^x-5e^{-x}-2>0 is x>ln(5/3)