Question

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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.

Answer

the natural log of e^x is x. Thus:
ln(e^x) = x
ln(e^2) = 2
ln (e^7) = 7
So this equation becomes:
x - 2 = 7
x = 9

Math

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

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