en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

ln(ln^2(x/e))=0

Solution

ln (ln^{2} (\frac{x}{e})) = 0

Solution

x = e^{2}, x = 1

+1

Decimal Notation

x = 7.38905 \dots, x = 1

Solution steps

ln (ln^{2} (\frac{x}{e})) = 0

Apply log rules

ln^{2} (\frac{x}{e}) = e^{0}

Rewrite the equation with

ln (\frac{x}{e}) = u

u^{2} = e^{0}

Solve

u^{2} = e^{0} : u = 1, u = - 1

u = 1, u = - 1

Substitute back

u = ln (\frac{x}{e}),

solve for

x

Solve

ln (\frac{x}{e}) = 1 : x = e^{2}

Solve

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

x = e^{2}, x = 1

Verify Solutions:

x = e^{2}

True

, x = 1

True

The solutions are

x = e^{2}, x = 1

Popular Examples

ln (y) = \frac{11}{5}

solvefor x,2log_{3}(3x-7)+1=9 solve for

x, 2 lo g_{3} (3 x - 7) + 1 = 9

1.8=-log_{10}(x)

1.8 = - lo g_{10} (x)

-9+log_{2}(2x)=-6

- 9 + lo g_{2} (2 x) = - 6

log_{2x+1}(49)=2

lo g_{2 x + 1} (49) = 2

Frequently Asked Questions (FAQ)

What is the answer to ln(ln^2(x/e))=0 ?
The answer to ln(ln^2(x/e))=0 is x=e^2,x=1