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Popular >

ln(x+e)-ln(x)=1

Solution

ln (x + e) - ln (x) = 1

Solution

x = \frac{e}{e - 1}

+1

Decimal Notation

x = 1.58197 \dots

Solution steps

ln (x + e) - ln (x) = 1

Add

ln (x)

to both sides

ln (x + e) - ln (x) + ln (x) = 1 + ln (x)

Simplify

ln (x + e) = 1 + ln (x)

Apply log rules

x + e = e x

Solve

x + e = e x : x = \frac{e}{e - 1}

x = \frac{e}{e - 1}

Verify Solutions:

x = \frac{e}{e - 1}

True

The solution is

x = \frac{e}{e - 1}

Popular Examples

log_{3}(81)-log_{3}(x-4)=2

lo g_{3} (81) - lo g_{3} (x - 4) = 2

ln (3 x - 12) = 4

log_{2}(6-x)-log_{2}(4-x)=2

lo g_{2} (6 - x) - lo g_{2} (4 - x) = 2

log_{5}(x-4)=1-log_{5}(x-8)

lo g_{5} (x - 4) = 1 - lo g_{5} (x - 8)

ln(x+2)+ln(x)=ln(6x)-ln(6)

ln (x + 2) + ln (x) = ln (6 x) - ln (6)

Frequently Asked Questions (FAQ)

What is the answer to ln(x+e)-ln(x)=1 ?
The answer to ln(x+e)-ln(x)=1 is x= e/(e-1)