How do you solve 2x=5x2?

1 Answer
Oct 29, 2016

How you do it is explained below.

Explanation:

Take the natural logarithm of both sides:

ln(2x)=ln(5x2)

Use the identity ln(ab)=ln(a)b

ln(2)x=ln(5)(x2)

Distribute ln(5):

ln(2)x=ln(5)x2ln(5)

Subtract ln(5)x from both sides:

(ln(2)ln(5))x=2ln(5)

Multiply both sides by -1:

(ln(5)ln(2))x=2ln(5)

Divide both sides by (ln(5)ln(2)):

x=2ln(5)ln(5)ln(2)

x3.5