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Popular >

ln(x)=log_{x}(e)

Solution

ln (x) = lo g_{x} (e)

Solution

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

+1

Decimal Notation

x = 2.71828 \dots, x = 0.36787 \dots

Solution steps

ln (x) = lo g_{x} (e)

Apply log rules

ln (x) = \frac{1}{ln ( x )}

Rewrite the equation with

ln (x) = u

u = \frac{1}{u}

Solve

u = \frac{1}{u} : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 1 : x = e

Solve

ln (x) = - 1 : x = \frac{1}{e}

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

Verify Solutions:

x = e

True

, x = \frac{1}{e}

True

The solutions are

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

Popular Examples

log_{3}(x+2)-log_{9}(x)=1

lo g_{3} (x + 2) - lo g_{9} (x) = 1

0.34 = ln (y)

log_{2}((r+9)^2)=6

lo g_{2} ((r + 9)^{2}) = 6

log_{3}(10-x)-log_{3}(x+2)=1

lo g_{3} (10 - x) - lo g_{3} (x + 2) = 1

log_{10}(y^{10})=2

lo g_{10} (y^{10}) = 2

Frequently Asked Questions (FAQ)

What is the answer to ln(x)=log_{x}(e) ?
The answer to ln(x)=log_{x}(e) is x=e,x= 1/e