LogIdentities - above? What if b = d instead? 1 Practice...

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Logarithmic and Exponential Identities Logarithms and exponentials are inverse functions. log( e a ) = a = e log( a ) Logarithms log( ab ) = log( a ) + log( b ) log( a b ) = b log( a ) You cannot simplify: log( a + b ) or log( a ) log( b ). Remember: the logarithm of a negative number is undefined. Challenge: how do you simplify log ± a b ² using these rules? Exponentials a b + c = a b a c a bc = ± a b ² c Also, ( ab ) c = a b c b You cannot simplify: a ( b c ) or a b + c d . There is no nice way to simplify: a b c d unless a = c or b = d . The not-nice way to simplify is a b c d = ± e log( a ) ² b ± e log( c ) ² d = e b log( a ) e d log( c ) = e b log( a )+ d log( c ) Challenge: if a = c how do you simplify a b c d using first three techniques
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Unformatted text preview: above? What if b = d instead? 1 Practice Here are some basic practice problems. Express the following expressions in terms of log(2), log(3) and powers of 2 and 3. 1. log 1 16 2. 4 x 3. e 2 log(2) 4. log(6) 5. 6 x 6. 2 x 2 y The following problems a bit more dicult. Simplify the following ex-pressions using the identities on this page. 1. log(4)-log 1 8 2. d dx 5 x and R 5 x dx 3. 8 x 4 y 4. e 3 log(3)-2 log(2) 2...
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This note was uploaded on 02/08/2011 for the course MATH 16B taught by Professor Sarason during the Fall '06 term at University of California, Berkeley.

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LogIdentities - above? What if b = d instead? 1 Practice...

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