document.write( "Question 276285: Given f(x)=3log6(2x-1) find f(5)to the nearest hundredth. \n" ); document.write( "

Algebra.Com's Answer #201458 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=3log%286%2C+%282x-1%29%29\"$
\n" ); document.write( " $\"f%285%29=3log%286%2C+%282%285%29-1%29%29\"$
\n" ); document.write( " $\"f%285%29=3log%286%2C+%2810-1%29%29\"$
\n" ); document.write( " $\"f%285%29=3log%286%2C+%289%29%29\"$
\n" ); document.write( "Now what do we do? How do we find a base 6 logarithm? No calculators I know can do base 6 logarithms. What we need to change the base to one our calculators \"know:. Fortunately there is a change of base formula for logarithms: $\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"$ . Using this to change our base 6 log into an expression of base 10 logs we get:
\n" ); document.write( " $\"f%285%29=3%28log%28%289%29%29%2Flog%28%286%29%29%29\"$
\n" ); document.write( "Now we can go to our calculators and find the two base 10 logarithms, divide them and then multiply by 3. (I'll leave that up to you to do.)

\n" ); document.write( "P.S. Many calculators also can do base e (ln) logarithms. If we used them instead of base 10 our equation would become:
\n" ); document.write( " $\"f%285%29=3%28ln%289%29%2Fln%286%29%29\"$
\n" ); document.write( "Believe it or not, this gives the same answer! (Try it if you don't believe it.) \n" ); document.write( "

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