Final answer:
The expression 2log(4)(7x)-log(4)(x+4)+log(4)(x-8) can be condensed using the properties of logarithms including exponents, product, and quotient rules to simplify it to a single logarithmic expression log(4)(((7x)^2)*(x-8)/(x+4)).
Step-by-step explanation:
The question pertains to the properties of logarithms. The expression that needs to be condensed is 2log4(7x) - log4(x+4) + log4(x-8). To condense this expression, we can apply the logarithmic properties.
Firstly, using the property of exponents in logarithms, we can rewrite the term with a coefficient as an exponent inside the logarithm:
Next, we apply the properties that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, and the logarithm of a quotient is the difference between the logarithms of the numerator and the denominator. The expression can be further condensed as follows:
- log4((7x)2) - log4(x+4) + log4(x-8) = log4(((7x)2)*(x-8)/(x+4))
This gives us the final condensed form of the logarithmic expression.