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What do expressions which use numbers or other symbols and an equal sign mean?
In mathematics, such expressions indicate that the value of the expression to the left of the equal sign has the same value as the expression to the right of the equal sign. In some cases, it can also be interpreted to mean that the expression on one side of the equal sign can be used in place of the expression on the other side of the equal sign (say in manipulating algebraic expressions). In computer languages, the equal sign is sometimes also used to indicate that the value of the expression to the right of the equal sign is to be transferred to the location indicated by the expression to the left of the equal sign. The expression to the left of the equal sign is usually a single variable that represents a memory location.
Are logarithmic functions rational expressions?
Sometimes :)
How can algebraic expressions be simplified?
In many ways. It really depends on the algebraic expression. If several terms are added/subtracted, you can usually combine similar terms (terms that have the same combination of variables). If variables are multiplied, you can combine the same variable, adding the corresponding exponents. Sometimes expressions get simpler if you factor them; sometimes you have to multiply out (in other words, the opposite of factoring). Quite frequently, you have to use a combination of methods to simplify expressions. Take an algebra book, and look at some of the examples.
Can an expression be solved?
Sometimes it can be simplified
Do you find principle square roots when you solve equations or expressions?
Yes, sometimes you need to do that.
