The solution to x-ln(x)>0 is x>0

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x-ln(x)>0

Solution

x - ln (x) > 0

x > 0

Interval Notation

(0, \infty)

Solution steps

x - ln (x) > 0

Move

x

to the right side

- ln (x) > - x

Multiply both sides by

- 1

ln (x) < x

For a>1, if

f (x) < g (x),

then

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

a = e

e^{l n (x)} < e^{x}

Simplify

e^{l n (x)} : x

x < e^{x}

Solve

x < e^{x} : x < e^{x}

x < e^{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

2 \geq 1 + ln (b)

lo g_{6} (x^{2}) \geq lo g_{6} (9)

lo g_{\frac{1}{2}} (lo g_{2} (\frac{x}{( 1 + x )})) > 0

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

lo g_{4} (- x) < 0