solve the follwing: ln e^3 + ln x^2 = ln (e^5)*x

First, we'll use the product property of the logarithmic
function, for the right side of the equality:

ln (e^5)*x =
ln (e^5) + ln x

Now, we can use the power property of the
logarithmic function:

 ln e^3 = 3* ln e, but ln e =
1

ln e^3 = 3

ln (e^5) = 5* ln
e, but ln e = 1

ln (e^5) =
5

ln x^2 = 2*ln x

We'll
re-write the equation:

3 + 2*ln x = 5 + ln
x

We'll isolate ln x to the
left:

2*ln x - ln x = 5-3

ln x
= 2

x =
e^2