The reverse process of expanding logarithms is called combining or condensing logarithmic expressions into a single quantity. The idea is that you are given a bunch of log expressions as sums and/or differences, and your task is to put them back or compress into a “nice” one log expression.

How do you condense logarithm?

Condense logarithmic expressions

1. Apply the power property first. Identify terms that are products of factors and a logarithm, and rewrite each as the logarithm of a power.
2. Next apply the product property. Rewrite sums of logarithms as the logarithm of a product.
3. Apply the quotient property last.

How to expand logarithmic expression?

There is no way to expand the logarithm of a sum or difference inside the argument of the logarithm. Rewrite the expression as an equation and express it as an exponential to give yourself some proof. From here, there is not much more you can do to make this expression more simple.

How to condense logarithm?

Rewrite radicals using rational exponents.

How to expand log expressions?

Expand a logarithm using a combination of logarithm rules. Condense a logarithmic expression into one logarithm. Taken together, the product rule, quotient rule, and power rule are often called “properties of logs.” Sometimes we apply more than one rule in order to expand an expression.

How to condense logs?

Let’s see how condensing log expressions works. Simplify log2(x) + log2(y). Since these logs have the same base, the addition outside can be turned into multiplication inside: log 2 (x) + log 2 (y) = log 2 (xy)