Table of Contents
What does it mean to condense a logarithmic expression?
The reverse process of expanding logarithms is called combining or condensing logarithmic expressions into a single quantity. Other textbooks refer to this as simplifying logarithms.
What are the properties of logarithms and examples?
In Mathematics, properties of logarithms functions are used to solve logarithm problems….Comparison of Exponent law and Logarithm law.
| Properties/Rules | Exponents | Logarithms |
|---|---|---|
| Product Rule | xp.xq = xp+q | loga(mn) = logam + logan |
| Quotient Rule | xp/xq = xp-q | loga(m/n) = logam – logan |
| Power Rule | (xp)q = xpq | logamn = n logam |
What is condense in math?
(tr) to increase the density of; compress. to reduce or be reduced in volume or size; make or become more compact.
How are the properties of exponents and logarithms related?
Logarithm of a Product 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.
How can logarithms be used to solve exponential equations?
1) Keep the exponential expression by itself on one side of the equation. 2) Get the logarithms of both sides of the equation. You can use any bases for logs. 3) Solve for the variable.
What do you mean by condense?
1 : to make or become more compact or concise Condense the paragraph into one sentence. 2 : to change or cause to change from a vapor to a liquid (as by cooling) The morning air condensed onto the cold window. condense. verb. con·dense | \ kən-ˈden(t)s \
How do you condense things?
Condensation happens one of two ways: Either the air is cooled to its dew point or it becomes so saturated with water vapor that it cannot hold any more water. Dew point is the temperature at which condensation happens. (Dew is simply condensed water in the atmosphere.)
What is condensing logarithms?
Condensing logarithms expression use the properties of logarithms to rewrite each expression as the logarithm of a single quantity. By condense the log, we really mean write it as a single logarithm with coefficient of one using logarithmic properties.
How do you expand a logarithmic equation?
Expanding of logarithmic problems using properties of logarithms to rewrite each expression as a sum, difference or multiple of logarithms. Turn the exponents from the inside of a logarithms into adding, subtracting or coefficients on the outside of the logarithm.
What is the difference between the two logarithmic expressions?
The difference between logarithmic expressions implies the Quotient Rule. I can put together that variable x and constant 2 inside a single parenthesis using division operation. Example 3: Combine or condense the following log expressions into a single logarithm:
How do you convert logarithms to rational exponents?
Step for Condensing Logarithms: Step 1: Apply Property 5 and move the number in front of the logarithm to the exponent of the variable. Step 2: Apply Property 3 or 4 to change the addition or subtraction of the logarithms to multiplication or division. Step 3: Rewrite rational exponents as radicals.