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Popular >

log_{2}(x)<x

Solution

lo g_{2} (x) < x

Solution

x > 0

+1

Interval Notation

(0, \infty)

Solution steps

lo g_{2} (x) < x

For a>1, if

f (x) < g (x),

then

a^{f (x)} < a^{g (x)}

a = 2

2^{l o g_{2} (x)} < 2^{x}

Simplify

2^{l o g_{2} (x)} : x

x < 2^{x}

Solve

x < 2^{x} : x < 2^{x}

x < 2^{x} :

True for all

x

True for all x

Find positive values for logs:

x > 0

Combine the intervals

True for all x and x > 0

Merge Overlapping Intervals

x > 0

Popular Examples

log_{10}(((x^2-36))/((48+22x-5x^2)))>= 0

lo g_{10} (\frac{( x ^{2} - 36 )}{( 48 + 22 x - 5 x ^{2} )}) \geq 0

log_{2}(((3x-4))/((x)))>1

lo g_{2} (\frac{( 3 x - 4 )}{( x )}) > 1

log_{6}(((x-2))/((6-x)))>0

lo g_{6} (\frac{( x - 2 )}{( 6 - x )}) > 0

lo g_{3} (y) + y < 4

ln (x - 1) \geq - 1

Frequently Asked Questions (FAQ)

What is log_{2}(x)<x ?
The solution to log_{2}(x)<x is x>0