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).
/* multiply both sides by 2 */
/* manipulate left site of equation using the properties of logarithms power rule */
/* simply */
/* raise both sides to the power of e. This gets rid of both the natural logs. */
/* multiply both sides by 4 */
/* subtract 4x */
/* pull out an x */
thus, we get x=4 or
Let's plug back in to check our solutions... starting with x=4
/* simplify the left side of the equation and rewrite ln(4) as ln(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
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.