### exercise in logarithm

Posted:

**Tue Mar 25, 2014 9:51 am**ln x/2 = (ln x)/2. How could this be solved???

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Posted: **Tue Mar 25, 2014 9:51 am**

ln x/2 = (ln x)/2. How could this be solved???

Posted: **Thu Mar 27, 2014 8:55 am**

y* ln( x ) = ln( x^y ) , so

1/2 * ln( x ) = ln ( x^( 1/2 ) ) = ln( sqrt( x ) )

Put that into your exercise and you get:

ln (x/2) = ln( sqrt(x) )

x/2 = sqrt(x)

x^2 / 4 = x

x*x = 4*x

x = 4

Tell me if I'm wrong, but i think this is the correct answer.

1/2 * ln( x ) = ln ( x^( 1/2 ) ) = ln( sqrt( x ) )

Put that into your exercise and you get:

ln (x/2) = ln( sqrt(x) )

x/2 = sqrt(x)

x^2 / 4 = x

x*x = 4*x

x = 4

Tell me if I'm wrong, but i think this is the correct answer.

Posted: **Thu Mar 27, 2014 10:32 am**

Yes...i think that's write.Thanks!

-- Sat Mar 29, 2014 10:44 am --

and that's a good solution too:

ln x/2 = (lnx)/2

lnx - ln2 = (lnx)/2

2ln x - 2ln 2 = 2(lnx)/2

2ln x - ln 2^2 = ln x

2ln x - ln x = ln 4

ln x =ln 4

x=4

-- Sat Mar 29, 2014 10:44 am --

and that's a good solution too:

ln x/2 = (lnx)/2

lnx - ln2 = (lnx)/2

2ln x - 2ln 2 = 2(lnx)/2

2ln x - ln 2^2 = ln x

2ln x - ln x = ln 4

ln x =ln 4

x=4

Posted: **Fri Aug 14, 2015 5:08 pm**

JProgress wrote:ln x/2 = (ln x)/2. How could this be solved???

x does equal 4. The above posters are correct, but they are missing a solution (which luckily does NOT work).

ln(x/2)=(lnx)/2

/* multiply both sides by 2 */

2ln(x/2)=lnx

/* manipulate left site of equation using the properties of logarithms power rule */

ln((x/2)^2)=lnx

/* simply */

ln(x^2/4)=lnx

/* raise both sides to the power of e. This gets rid of both the natural logs. */

x^2/4=x

/* multiply both sides by 4 */

x^2=4x

/* subtract 4x */

x^2-4x=0

/* pull out an x */

x(x-4)=0

thus, we get x=4 or x=0.

Let's plug back in to check our solutions... starting with x=4

ln(4/2)=ln(4)/2

/* simplify the left side of the equation and rewrite ln(4) as ln(2^2) */

ln(2)=ln(2^2)/2

/* using the power rule we can rewrite ln(2^2) as 2ln(2) */

ln(2) = 2ln(2)/2

/* simplify to right side of the equation (2 * 1/2 = 1)

we are left with ln(2)=ln(2), so x=4 is correct!

Now onto x=0

ln(0/2)=ln(0)/2

We can already stop because ln(0) DNE... When x=0 the equation DNE. This is because ln(0)=x can be rewritten as e^x=0, and no value of x satisfies that equation.