Question

can someone explain what Exponentiate both sides means??

Answer 1

example:
ln (x + 4) + ln (x - 2) = ln 7


First we use property 1 of logarithms to combine the terms on the left.

ln (x + 4)(x - 2) = ln 7


Now apply the exponential function to both sides.
eln (x + 4)(x - 2) = eln 7
The logarithmic identity 2 allows us to simplify both sides.
(x + 4)(x - 2) = 7
x2 + 2x - 8 = 7
x2 + 2x - 15 = 0
(x - 3)(x + 5) = 0
x = 3 or x = -5
x = 3 checks, for ln 7 + ln 1 = ln 7.
x = -5 does not check, for when we try to substitute -5 for x in the original equation
we are taking the natural logarithm of negative numbers, which is not defined.
So, x = 3 is the only solution.

Answer 2

Hope that helps some.