Simplify each of the following:
a). ln(1/√ e^5)
b. ln (e^4e^2/e^3)
c. e^ln(x+5)
d. e^lnx+ln2
e. e^ln15-ln3
If you can only help me with a couple any help is appreciated! Thanks!!
a. ln (1/√ e^5) = ln e^(-5/2) = -5/2
b. ln (e^4e^2/e^3) = ln e^6/e^3 = ln e^3 = 3
c. e^ln(x+5) = x + 5
d. e^(ln x+ln 2) = ln x + ln 2 = ln 2x
e. e^(ln15 - ln 3) = e^(ln 15/3) = 15/3 = 5
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Verified answer
a. ln (1/√ e^5) = ln e^(-5/2) = -5/2
b. ln (e^4e^2/e^3) = ln e^6/e^3 = ln e^3 = 3
c. e^ln(x+5) = x + 5
d. e^(ln x+ln 2) = ln x + ln 2 = ln 2x
e. e^(ln15 - ln 3) = e^(ln 15/3) = 15/3 = 5