document.write( "Question 815816: 5 log 3 + log 4 in single logarithm
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Algebra.Com's Answer #491274 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
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  • To go from two logs to one we need to either eliminate one of them or find a way to combine them. There's no way to eliminate a log from this expression so we will have to combine them.
  • There are two ways to combine logs:
    • Algebraically add them. This requires that the bases and arguments of the logs are the same. The bases of our logs are the same, 10, but the arguments are different, 3 and 4. Since there is no way to make the arguments be the same we will not be able to add the logs algebraically.
    • Use the \"log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Aq%29%29\" property of logs. This property requires that the logs have the same bases (which ours do) and have coefficients of 1 (which ours do not since the first log has a coefficient of 5). Fortunately there is a way to change the coefficient to a 1.
  • A property of logs, \"n%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5En%29%29\", allows one to \"move\" a coefficient into the argument as its exponent. This is how we will handle the 5.
So our plan is to move the 5 using one property and then combine the logs using the other:
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\n" ); document.write( "Now we can use the other property to combine them:
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\n" ); document.write( "which simplifies to:
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