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Popular >

solvefor x,(xy)^x=e

Solution

solve for

x, (x y)^{x} = e

Solution

x = \frac{1}{W ( y )}

Solution steps

(x y)^{x} = e

Prepare

(x y)^{x} = e

for Lambert form:

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

Rewrite the equation with

\frac{1}{x} = u

and

x = \frac{1}{u}

\frac{1}{u} y e^{- u} = 1

Rewrite

(\frac{1}{u}) y e^{- u} = 1

in Lambert form:

u e^{u} = y

Solve

u e^{u} = y : u = W (y)

Verify Solutions:

u = W (y)

True

The solution is

u = W (y)

Substitute back

u = \frac{1}{x},

solve for

x

Solve

\frac{1}{x} = W (y) : x = \frac{1}{W ( y )}

x = \frac{1}{W ( y )}

Popular Examples

2^{2x+4}=3^{x-24}

2^{2 x + 4} = 3^{x - 24}

2^{2-x}=5^{x+1}

2^{2 - x} = 5^{x + 1}

2^{n} = 100

8*2^{x+1}=2^{2x}

8 \cdot 2^{x + 1} = 2^{2 x}

1/(6^{x-1)}=216

\frac{1}{6 ^{x - 1}} = 216

Frequently Asked Questions (FAQ)

What is the answer to solvefor x,(xy)^x=e ?
The answer to solvefor x,(xy)^x=e is x= 1/(\W(y))