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x = 1/16

Step-by-step explanation:

Since the inverse of a Logarithm is an exponential function, we know that the final solution has to involve an exponential function somewhere in it.

1. log B(2) {x} = -4  || given

2. x = 2 ^ -4  || Logarithm rule that allows you to move the base of the logarithm to the base of the exponent on the other side. For example, if you had log B(5) {x} = 3, the base of 5 would move over to the other side and it would be raised to 3; x = 5^3.

3. x = (1) / (2^4) || Simplify. Use the negative exponent rule. This rule always leaves a numerator of 1, and a denominator of your exponent. In this case, it will be 2 ^ -4, so you will do 2^4 which is 16 and you will put that over 1. Resulting in your final answer of x = 1/16

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