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Popular >

ln(x)<= x-1

Solution

ln (x) \leq x - 1

Solution

x > 0

+1

Interval Notation

(0, \infty)

Solution steps

ln (x) \leq x - 1

For a>1, if

f (x) \leq g (x),

then

a^{f (x)} \leq a^{g (x)}

a = e

e^{l n (x)} \leq e^{x - 1}

Simplify

e^{l n (x)} : x

x \leq e^{x - 1}

Solve

x \leq e^{x - 1} : x \leq e^{x - 1}

x \leq e^{x - 1} :

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_{2}(x+1)))/((x-1))>0

\frac{( lo g _{2} ( x + 1 ) )}{( x - 1 )} > 0

log_{3}(x^2-8x)<2

lo g_{3} (x^{2} - 8 x) < 2

log_{2}(1+x^{-1})+log_{1/2}((1+x)/4)>= 1

lo g_{2} (1 + x^{- 1}) + lo g_{\frac{1}{2}} (\frac{1 + x}{4}) \geq 1

x - ln (x) > 0

2 \geq 1 + ln (b)

Frequently Asked Questions (FAQ)

What is ln(x)<= x-1 ?
The solution to ln(x)<= x-1 is x>0