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What is the answer to the following equation using logarithms 13 to the power of x equals -169 find x?
Louis54321
182
Beryl Cassin
Wiki User
∙ 13y agoThis is a bit tricky, since you can't take the logarithm of a negative number. If you change the -169 to +169, you get:
13x = 169
Taking logarithms to base 10:
log(13x) = log 169
or:
x log 13 = log 169
x times 1.11 = 2.22
x = 2
(Note: In this particular case, we could have obtained the number 2 much faster through inspection, since we know - or can quickly confirm - that 13 squared is equal to 169. However, these techniques can also be used for other, more difficult cases.)
Since in the real numbers you can't take the logarithm of a negative number, I would say that this problem has no solution - at least, not in the real numbers. However, if you are willing to accept complex solutions, you can take the logarithms on both sides. This is similar to the above, but in the case of a negative number, you would get a complex solution.
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