Final answer:
The expression g log(a) - log(d) can be condensed using the logarithm properties of exponentiation and division, resulting in log(a^g/d). However, none of the provided options match this correct condensation.
Step-by-step explanation:
The question is asking to condense the logarithmic expression g log(a) - log(d). To condense this expression, we can use two properties of logarithms:
- The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This is written as log(a^b) = b log(a).
- The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, which is log(a/b) = log(a) - log(b).
Applying these properties to the given expression, we can rewrite g log(a) as log(a^g). Then, using the difference property, we can combine the terms to get:
log(a^g/d)
However, as there is no option that directly matches this result, we must remember that raising a number to the power of another number is the same as multiplying the logarithms of the respective numbers. Therefore, g log(a) is equivalent to log(a^g) and not log(g * a). Therefore, none of the provided options are correct for the given expression g log(a) - log(d).