Exponential laws logrithm function.

[italian1013]

find x for y=5

y = -(((e^x)/(e^-x))/2) + ((e^x)/(e^(-3x))

all i did was a^m / a^n = a^m-n

i get here y = -1/2(e^(2x)) + (e^(4x))
after this i get iffy and want to make sure i can do what i did.

5 = -1/2(e^(2x)) + (e^(4x))
ln|5|= -1/2(ln(e^2x)) + ln(e^4x)
ln|5|= -1/2(2x) + 4x
ln|5|= -x + 4x
ln|5|= 3x

x = ln|5|/3

is this right?

 

[Mentallic]

$$ln(a+b)\neq ln(a)+ln(b)$$

Substitute $$u=e^{2x}$$