3 ln 2x = 9 solve for x?

Answer 1

ln (2x) = 3
2x = e³
x = e³ / 2

Answer 2

3

Answer 3

When multiplying numbers, you can add their logs.

log(A*B) = log(A) + log(B).

Therefore,
3 ln(2x) = ln(2x) + ln(2x) + ln(2x) =
ln ( 2x*2x*2x ) = ln ( 8 x^3)

we now have
ln(8 x^3) = 9

if a = b
then
e^a = e^b
(we can raise e to the power of each side and retain an equality)

also
e^ln(A) = A

The natural logarithm of a number is the power to which one would have to raise e in order to find the number; therefore, raising e to the power of the natural log of a number gives that number.

e^ln(8 x^3) = e^9
8 x^3 = e^9
x^3 = (e^9) / 8

e^9 = e^3 * e^3 * e^3 = (e^3)^3
and
8 = 2^3

x^3 = [ (e^3) / 2 ]^3

cube root both sides

x = e^3 / 2 = (1/2) * e^3 = approximately 10.

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check with 10

3 ln(20) = 3*2.9957... = 8.9872... close to 9

a closer answer would be
10.042768

3*ln(20.085536) = 3*3 = 9 (to the accuracy of my calculator)

Answer 4

Divide each side by 2...
so 2x divided by two and 9 divided by 2 is:
x=9/2
Or 4 1/2 in a mixed fraction.
Or 4.5 as a decimal :D

Answer 5

First off divide each side by 3 to get:

ln(2x)=3

Then raise each side to 'e' power

e^ln(2x)=e^3 e^ln(___) is equal to whatever is inside so:

2x = e^3 Divide each side by 2

x = [e^(3)]/2

Answer 6

x=4.5 of course. 2x divided by 2 cancels out. 9/2 gives you 4.5 or 4 1/2.

Answer 7

x=4.5