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Popular >

5^{x^2}>2^x

Solution

5^{x^{2}} > 2^{x}

Solution

x < 0 or x > \frac{ln ( 2 )}{ln ( 5 )}

+2

Interval Notation

(- \infty, 0) \cup (\frac{ln ( 2 )}{ln ( 5 )}, \infty)

Decimal Notation

x < 0 or x > 0.43067 \dots

Solution steps

5^{x^{2}} > 2^{x}

If

f (x) > g (x)

then

ln (f (x)) > ln (g (x))

ln (5^{x^{2}}) > ln (2^{x})

Simplify

ln (5^{x^{2}}) : ln (5) x^{2}

Simplify

ln (2^{x}) : ln (2) x

ln (5) x^{2} > ln (2) x

ln (5) x^{2} > ln (2) x : x < 0 or x > \frac{ln ( 2 )}{ln ( 5 )}

x < 0 or x > \frac{ln ( 2 )}{ln ( 5 )}

Popular Examples

-2/3 ln(1-9^{3/2})=0+C

- \frac{2}{3} ln (1 - 9^{\frac{3}{2}}) = 0 + C

factor 4-x^2 factor

4 - x^{2}

\frac{3}{2} x = 1

simplify \sqrt[6]{x^3y^{18}}simplify

simplify (1/8)^{4/3}simplify

(\frac{1}{8})^{\frac{4}{3}}

Frequently Asked Questions (FAQ)

What is 5^{x^2}>2^x ?
The solution to 5^{x^2}>2^x is x<0\lor x>(ln(2))/(ln(5))