How can you use the properties of logarithms to condense logarithmic expressions?
- Apply the power property first. Identify terms that are products of factors and a logarithm, and rewrite each as the logarithm of a power.
- Next apply the product property. Rewrite sums of logarithms as the logarithm of a product.
- Apply the quotient property last.
Hereof, what does it mean to condense a logarithmic expression?
When they tell you to "simplify" a log expression, this usually means they will have given you lots of log terms, each containing a simple argument, and they want you to combine everything into one log with a complicated argument. "Simplifying" in this context usually means the opposite of "expanding".
One may also ask, how do you do properties of logarithms?
The logarithm of a product property says log2 8a = log2 8 + log2 a, and log2 8 = 3. You can use the similarity between the properties of exponents and logarithms to find the property for the logarithm of a quotient. With exponents, to multiply two numbers with the same base, you add the exponents.
The laws apply to logarithms of any base but the same base must be used throughout a calculation. This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. The same base, in this case 10, is used throughout the calculation.