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Popular >

e^6x=6e^x

Solution

e^{6} x = 6 e^{x}

Solution

x = 6, x = - W_{0} (- \frac{6}{e ^{6}})

+1

Decimal Notation

x = 6, x = 0.01509 \dots

Solution steps

e^{6} x = 6 e^{x}

Prepare

e^{6} x = 6 e^{x}

for Lambert form:

e^{6 - x} x = 6

Rewrite the equation with

- x = u

and

x = - u

e^{6 - (- u)} (- u) = 6

Simplify

- e^{6 + u} u = 6

Rewrite

- e^{6 + u} u = 6

in Lambert form:

e^{u} u = - \frac{6}{e ^{6}}

Solve

e^{u} u = - \frac{6}{e ^{6}} : u = - 6, u = W_{0} (- \frac{6}{e ^{6}})

u = - 6, u = W_{0} (- \frac{6}{e ^{6}})

Substitute back

u = - x,

solve for

x

Solve

- x = - 6 : x = 6

Solve

- x = W_{0} (- \frac{6}{e ^{6}}) : x = - W_{0} (- \frac{6}{e ^{6}})

x = 6, x = - W_{0} (- \frac{6}{e ^{6}})

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2^{-(x+3)}=32^x

2^{- (x + 3)} = 3 2^{x}

Frequently Asked Questions (FAQ)

What is the answer to e^6x=6e^x ?
The answer to e^6x=6e^x is x=6,x=-\W_{0}(-6/(e^6))