Final answer:
To condense 3 log c - y log d, you convert the coefficients into exponents of the respective term and subtract the two terms under a single logarithm, resulting in log(c^3/d^y). This uses logarithm power and quotient rules.
Step-by-step explanation:
To condense the logarithm of 3 log c - y log d, you'll need to apply a few logarithmic properties. Specifically, you can use the property that allows you to move the coefficient of the logarithm inside as an exponent of the argument. This is because the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (logarithm power rule).
Using this property:
- The term 3 log c becomes log(c^3).
- Similarly, the term y log d becomes log(d^y).
- Now apply the property that states the logarithm resulting from the division of two numbers is the difference between the logarithms of the two numbers (logarithm quotient rule). Thus, 3 log c - y log d can be condensed to log(c^3/d^y).
Example:
If you have an expression like 2 log 5 - 3 log 2, you would condense it to log(5^2) - log(2^3), which simplifies further into log(25/8)