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log log log + = 2 100 log 2log 50log = = + Think: Multiply two numbers with the same base, add the exponents. Think: Divide two numbers with the same base, Properties of Logarithms (Recall that logs are only defined for positive values of x.) For the natural logarithm For logarithms base a. 1. lnxy = lnx + lny. 1. The notation is read “the logarithm (or log) base of .” The definition of a logarithm indicates that a logarithm is an exponent. is the logarithmic form of.4. log 3. √. 100x2 yz5. 5. log117(x2 − 4). Solution. 1. To expand log2. (8 x), we use the Quotient Rule identifying u = 8 and w = x and simplify. Solve the following logarithmic equations. (1) lnx = −3. (2) log(3x − 2) = 2. (3) 2 log x Example 1: Use the Laws of Logarithms to rewrite the expression in a form with no logarithm of a product, quotient, or power. (a). 3. 3. 2. 5 log x y. explain what is meant by a logarithm. • state and use the laws of logarithms. • solve simple equations requiring the use of logarithms. Contents. Rules for logarithms. The most important rule for exponential functions is axay = ax+y. Because loga(x) is the inverse of ax, it satisfies the “opposite” of