Solve the logarithmic equation, log (n + 9) = log 4n, log -5x = log (10 - 3x) and log (-3m - 1) = log (-4m -6)?
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If log x = log y, then x = y. So for each of these problems, because you're taking a single logarithm of everything on both sides, you can just drop the "log" from each side and then solve what's left. However, then you have to check the solution in the original problem to verify that logs are only being taken of positive numbers; otherwise, the values are outside the domain of the original equation, as one may only take the logarithms of positive numbers.
log (n + 9) = log 4n
n + 9 = 4n
9 = 3n
3 = n
Answer: n = 3 (which results in log 12 = log 12, and 12 is positive and therefore valid.)
log -5x = log (10 - 3x)
-5x = 10 - 3x
-10 = 2x
-5 = x
Answer: x = -5 (which results in log 25 = log 25, and 25 is positive and therefore valid.)
log (-3m + 1) = log (-4m - 6)
-3m + 1 = -4m - 6
m = -7
Answer: m = -7 (which results in log 22 = log 22, and 22 is positive and therefore valid.)