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Popular >

ln(x+1)<x

Solution

ln (x + 1) < x

Solution

- 1 < x < 0 or x > 0

+1

Interval Notation

(- 1, 0) \cup (0, \infty)

Solution steps

ln (x + 1) < x

For a>1, if

f (x) < g (x),

then

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

a = e

e^{l n (x + 1)} < e^{x}

Simplify

e^{l n (x + 1)} : x + 1

x + 1 < e^{x}

Solve

x + 1 < e^{x} : x < 0 or x > 0

Find positive values for logs:

x > - 1

Combine the intervals

(x < 0 or x > 0) and x > - 1

Merge Overlapping Intervals

- 1 < x < 0 or x > 0

Popular Examples

log_{10}(x+5)>1

lo g_{10} (x + 5) > 1

ln (x - 2) \geq - 3

lo g_{3} (x + 2) < 1

log_{10}(2x)<log_{10}(x+6)

lo g_{10} (2 x) < lo g_{10} (x + 6)

log_{0.5}(x^2-4x+3)<= 1

lo g_{0.5} (x^{2} - 4 x + 3) \leq 1

Frequently Asked Questions (FAQ)

What is ln(x+1)<x ?
The solution to ln(x+1)<x is -1<x<0\lor x>0