Math Problem 4(lnx)^2 = lnx^2?

anonymous

I can't figure out how to solve this problem. My book says I need to answer the problem exactly without using a calculator.

The problem is : 4(lnx)^2 = lnx^2

Help would be really appreciated!

mein-hoon-na

we know ln (a^y) = y ln a

so 4(ln x)^2 = ln x^2 = 2 ln x

or 2 ln x = 1

or ln x = 1/2

or x = e^(1/2)

mark

4(lnx)² = lnx²

Bring the exponent in the proudt out as an coefficient:

4(lnx)² = 2lnx

divide both sides by (lnx)²:

4 = 2lnx / (lnx)²

lnx reduces out in the numerator since it is a factor in the numerator and denominator:

4 = 2/ lnx

cross multiply:

4lnx = 2

divide both sides by 4:

lnx = 2/4

reduce the fraction:

lnx = 1/2

change to exponential form:

e^(1/2) = x