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Popular >

2x=e^2ln(x)

Solution

2 x = e^{2} ln (x)

Solution

x = e^{2}, x = - \frac{e ^{2} W _{0} ( - \frac{2}{e ^{2}} )}{2}

+1

Solution steps

2 x = e^{2} ln (x)

Switch sides

e^{2} ln (x) = 2 x

Divide both sides by

e^{2}

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

If

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x)} = e^{\frac{2 x}{e ^{2}}}

Simplify

e^{l n (x)} : x

x = e^{\frac{2 x}{e ^{2}}}

Solve

x = e^{\frac{2 x}{e ^{2}}} : x = e^{2}, x = - \frac{e ^{2} W _{0} ( - \frac{2}{e ^{2}} )}{2}

x = e^{2}, x = - \frac{e ^{2} W _{0} ( - \frac{2}{e ^{2}} )}{2}

Verify Solutions:

x = e^{2}

True

, x = - \frac{e ^{2} W _{0} ( - \frac{2}{e ^{2}} )}{2}

True

The solutions are

x = e^{2}, x = - \frac{e ^{2} W _{0} ( - \frac{2}{e ^{2}} )}{2}

Popular Examples

log_{10}(x)=7.6348

lo g_{10} (x) = 7.6348

5 = lo g_{x} (32)

lo g_{7} (x) = 21

0.9 = ln (y)

log_{2}(x+5)-log_{2}(6)=3

lo g_{2} (x + 5) - lo g_{2} (6) = 3

Frequently Asked Questions (FAQ)

What is the answer to 2x=e^2ln(x) ?
The answer to 2x=e^2ln(x) is x=e^2,x=-(e^2\W_{0}(-2/(e^2)))/2