Final answer:
The expression 5 log(b)q - log(b)r can be condensed into a single logarithm using properties of logarithms: log(b)(q^5/r), which is the result of applying exponentiation to the first term and the logarithmic property of division.
Step-by-step explanation:
To condense the expression 5 log(b)q - log(b)r into a single logarithm, we can apply two properties of logarithms. The first property is that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. The second property is the logarithm of a division, expressed as the difference between the logarithms of the numerator and the denominator.
Applying these properties, we can rewrite the expression as:
log(b)q^5 - log(b)r
According to the property of logarithms regarding division, this can be further condensed into:
log(b)(q^5/r)
So the condensed form of the given expression is logb(q^5/r).