Final answer:
To combine log(3) and log(4) into a single logarithm, we use the property that the sum of two logarithms with the same base is the logarithm of the product of their arguments.
Step-by-step explanation:
To combine into a single logarithm, we use the properties of logarithms. Given the options, let's use these properties to determine the correct combination:
The property mentioned in the third information point is that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. However, this property does not help us to combine the given logs because there are no exponents involved in this problem.
According to another property of logarithms (stated in information point 35), the sum of two logarithms with the same base can be written as the logarithm of the product of their arguments. Mathematically, we express this as log(a) + log(b) = log(a × b). Applying this property to option (a) log(3)+log(4), we get log(3 × 4), which simplifies to log(12).
Option (b), log(3)−log(4), is the difference of two logarithms, which corresponds to the division of their arguments, represented as log(a) - log(b) = log(a / b). Hence this option simplifies to log(3/4).
Options (c) and (d) already represent single logarithms, so no further action is needed to combine them.
So, the correct answer that represents combining log(3) and log(4) into a single logarithm is option (c) log(3×4), which is log(12).