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Popular >

(log_{e}(x)-1)^2=4

Solution

(lo g_{e} (x) - 1)^{2} = 4

Solution

x = e^{3}, x = \frac{1}{e}

+1

Decimal Notation

x = 20.08553 \dots, x = 0.36787 \dots

Solution steps

(lo g_{e} (x) - 1)^{2} = 4

Rewrite the equation with

lo g_{e} (x) = u

(u - 1)^{2} = 4

Solve

(u - 1)^{2} = 4 : u = 3, u = - 1

u = 3, u = - 1

Substitute back

u = lo g_{e} (x),

solve for

x

Solve

lo g_{e} (x) = 3 : x = e^{3}

Solve

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

x = e^{3}, x = \frac{1}{e}

Verify Solutions:

x = e^{3}

True

, x = \frac{1}{e}

True

The solutions are

x = e^{3}, x = \frac{1}{e}

Popular Examples

n-8log_{2}(n)=0

n - 8 lo g_{2} (n) = 0

log_{2}(72x)-log_{2}(x+96)=3

lo g_{2} (72 x) - lo g_{2} (x + 96) = 3

lo g_{4} (y) = 1

ln(x)+ln(2x)=ln(450)

ln (x) + ln (2 x) = ln (450)

-4log_{2}(5x)=12

- 4 lo g_{2} (5 x) = 12

Frequently Asked Questions (FAQ)

What is the answer to (log_{e}(x)-1)^2=4 ?
The answer to (log_{e}(x)-1)^2=4 is x=e^3,x= 1/e