document.write( "Question 172949: Evaluate the following expressions:\r
\n" ); document.write( "\n" ); document.write( "log3 81\r
\n" ); document.write( "\n" ); document.write( "log5 1/25\r
\n" ); document.write( "\n" ); document.write( "ln e^4\r
\n" ); document.write( "\n" ); document.write( "log.01 \n" ); document.write( "

Algebra.Com's Answer #127817 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
The rule you need to apply in each case is $\"log%28b%2C%28y%29%29=x\"$ if and only if $\"b%5Ex=y\"$ .\r
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\n" ); document.write( "\n" ); document.write( "I'll show you the first one:\r
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\n" ); document.write( "\n" ); document.write( " $\"log%283%2C%2881%29%29=x\"$ if and only if $\"3%5Ex=81\"$ . So what does x have to be so that $\"3%5Ex=81\"$ ? Since $\"3%2A3%2A3%2A3=3%5E4=81\"$ , $\"x=4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Work the rest of them the same way. Note that $\"ln%28x%29=log%28e%2C%28x%29%29\"$ ( $\"e\"$ is the base of the natural logarithms) and $\"log%28x%29\"$ (no base specified) is the same as $\"log%2810%2C%28x%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "You might also want to make use of the rule $\"log%28b%2C%28x%5En%29%29=n%2Alog%28b%2C%28x%29%29\"$ and remember that $\"x%5E1=x\"$ for all real $\"x\"$ . \n" ); document.write( "

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