Question

-6 + log₃(-2x) = -5)
a) x = -1/2
b) x = -1
c) x = 1/2
d) x = 1

Answer 1

The solution to the equation -6 + log₃(-2x) = -5 is x = -1.5, which does not match any of the options provided. It seems there may be a typo in the question or the answer choices.

Step-by-step explanation:

To solve the equation -6 + log₃(-2x) = -5, we first need to isolate the logarithm on one side of the equation. We do this by adding 6 to both sides, giving us log₃(-2x) = 1. The next step is to rewrite the equation in exponential form, which is the inverse of taking the logarithm. The exponential form of this equation is 3¹ = -2x, or -2x = 3. Now, we can solve for x by dividing both sides by -2, which gives us: x = -3/2 or x = -1.5. However, none of the options provided in the question match this solution, which suggests there might have been a typo in the original problem or the options given.