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3 years ago

Solve the following logarithmic equations log(x) + log(−x) = 0

Mathematics

1 answer:

slavikrds [6]3 years ago

3 0

Answer:

x= +i and x = -i

Step-by-step explanation:

First we use the property of a sum of logarithms (the sum of two logarithms is equal to multiplying them) and we have that

log (x) + log (-x) = 0

log((x)(-x)) = 0

log (-x²) = 0

we can write this as an exponential equation. ( When you have a single logarithm on one side of the equation then you can express it as an exponential equation and solve)

-x²= 10⁰

-x²= 1

x²= -1

x= ±i

Therefore the solutions are x= +i and x = -i

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