## What is the subtraction property of logarithms?

To subtract logs, just divide the inputs (numbers inside the log). The rule logb(x/y) = logb(x) – log_b(y) lets you “convert division to log subtraction”. It’s actually just the “log version” of the quotient rule for exponents.

## What are exponential properties?

Exponential Properties: Quotient of like bases: To divide powers with the same base, subtract the exponents and keep the common base. 3. Power to a power: To raise a power to a power, keep the base and multiply the exponents. Zero exponent: Any number raised to the zero power is equal to “1”.

How do you use the properties of logarithms?

You will get the same answer that equals 2 by using the property that logb bx = x. Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms.

What are properties of logarithms?

Properties of Logarithms

1. loga (uv) = loga u + loga v 1. ln (uv) = ln u + ln v
2. loga (u / v) = loga u – loga v 2. ln (u / v) = ln u – ln v
3. loga un = n loga u 3. ln un = n ln u

### How to find the properties of a logarithm?

Let us compare here both the properties using a table: Properties/Rules Exponents Logarithms Product Rule x p .x q = x p+q log a (mn) = log a m + log a n Quotient Rule x p /x q = x p-q log a (m/n) = log a m – log a n Power Rule (x p) q = x pq log a m n = n log a m

### When does the exponent of a logarithm become a coefficient?

Only when the argument is raised to a power can the exponent be turned into the coefficient. When the entire logarithm is raised to a power, then it can not be simplified. (log a x) r ≠ r * log a x The log of a quotient is not the quotient of the logs. The quotient of the logs is from the change of base formula.

How is the log of a product related to the exponents?

The log of a product is the sum of the logs. log a xy = log a x + log a y The rule when you divide two values with the same base is to subtract the exponents. Therefore, the rule for division is to subtract the logarithms. The log of a quotient is the difference of the logs.

Can a product rule be used to expand a logarithm?

We can use the product rule to rewrite logarithmic expressions. For our purposes, expanding a logarithm means writing it as the sum of two logarithms or more. Let’s expand . Notice that the two factors of the argument of the logarithm are and . We can directly apply the product rule to expand the log.