You can put this solution on YOUR website! For this problem the task is to express the 20 as a product, quotient or power of some combination of the "known" logarithms. The "known" logarithms are the ones you are given, >i>plus the log of the base of logarithms you are working with.
In this problem you were given expressions to use for log(2) and log(3). These are base 10 logs so you can also use log(10). The logs we can use are:
log(2) = m
log(3) = n
log(10) = 1
Now we try to figure out how to express 20 as a product, quotient or power of some combination of 2's. 3's and/or 10's. It should not take long to figure out that 20 = 2*10. So
log(20) = log(2*10)
Now we use a property of logarithms, , to split the log of the product into the sum of the logs of the factors:
log(20) = log(2*10) = log(2) + log(10)
Since log(2) = m and log(10) = 1 this becomes:
log(20) = log(2*10) = log(2) + log(10) = m + 1
which is the desired expression.
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