ln e^x - ln e^2 = ln e^7

We know that ln e^x = xlne

Also we know that ln e = 1

Now let us substitute:

x ln e -2ln e = 7 ln e

x*1 -2*1 = 7*1

==> x-2 = 7

Add 2 to both sides:

==> x = 7+2 = 9

**The answer is x=9**

The equation ln e^x - ln e^2 = ln e^7 has to be solved.

ln e^x - ln e^2 = ln e^7

Use the property of logarithm log a^b = b*log a.

x*ln e - 2*ln e = 7*ln e

ln e*(x - 2) = ln e*7

Now ln is used to denote natural logarithm or log to the base e. Now use the property log_b b = 1. This gives:

x - 2 = 7

x = 2 + 7

x = 9

The solution of the equation is x = 9

First, let's recall the property that ln e =1.

Now, we'll use the power property of logarithms, so that:

ln e^2 = 2ln e =2

ln e^7 = 7ln e = 7

ln e ^x = xln e = x

Now, we'll re-write the equation:

x - 2 = 7

We'll add 2 both sides:

x = 7+2

**x = 9**

lne^x - lne^2=lne^7.

Solution:

By definition, ln e^a = a.

So lne^x =x, lne^2 =2 and lne^7 =7. Therefore the given equation could now be rewritten as:

x -2=7 Or

x = 7+2 = 9.