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QUESTION

# How do you solve ln e^x -ln e^3 = ln e^9?

If you use the properties of logarithms, you will need to refer to these:

1. lna^b = blna
2. lne = 1

OR

lne^z = z

where a and b are constants, e = 2.718281828cdots, and z is either a constant or a variable. Therefore, we can do this:

lne^x - lne^3 = lne^9

lne^x = lne^9 + lne^3

xcancel(lne) = 9cancel(lne) + 3cancel(lne)

color(blue)(x) = 9 + 3 = color(blue)(12)