document.write( "Question 609701: given log base[c](2)=0.431 and logbase[c](3)=0.683 find log[c](108/25) \n" ); document.write( "

Algebra.Com's Answer #383962 by jsmallt9(3758) $\"\"$ $\"About$

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To find an answer to this problem we need to be able to rewrite 108/25 in terms of powers, products and/or quotients of 2's and/or 3's and/or c's. Since there is no way to to this with the 25, I am assuming that the 25 is supposed to be 24 or 27. I'm guessing 24. (In the future, be sure to check what what you've typed before posting it.)

\n" ); document.write( "Rewriting 108/24 in terms of 2's and 3's:
\n" ); document.write( " $\"log%28c%2C+%28%282%5E2%2A3%5E3%29%2F%282%5E3%2A3%29%29%29\"$
\n" ); document.write( "Now we start using properties of logarithms to rewrite this in terms of logs of 2 and 3. First we'll use the property for quotients:
\n" ); document.write( " $\"log%28c%2C+%282%5E2%2A3%5E3%29%29+-+log%28c%2C+%282%5E3%2A3%29%29\"$
\n" ); document.write( "Next the property for products:
\n" ); document.write( "

\n" ); document.write( "Note the use of parentheses! It is important to use them when making substitutions of multiple terms for parts of an expression. (Here we are substituting two term expressions.
\n" ); document.write( "Next we use the property for powers of the argument:
\n" ); document.write( "

\n" ); document.write( "Now that we have everything in terms of logs of 2 and 3, we can start substituting in the given values. Or you could start combining like terms first. I'm going to combine like terms first. Distributing the \"-\" we get:
\n" ); document.write( "

\n" ); document.write( "Combining the like terms we get:
\n" ); document.write( " $\"-log%28c%2C+%282%29%29+%2B+2%2Alog%28c%2C+%283%29%29\"$
\n" ); document.write( "Substituting in the given values:
\n" ); document.write( "-(0.431) + 2*(0.683)
\n" ); document.write( "0.935

\n" ); document.write( "So $\"log%28c%2C+%28108%2F24%29%29+=+0.935\"$ \n" ); document.write( "

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