SOLUTION: given log base[c](2)=0.431 and logbase[c](3)=0.683 find log[c](108/25)

Question 609701: given log base[c](2)=0.431 and logbase[c](3)=0.683 find log[c](108/25)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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.)

Rewriting 108/24 in terms of 2's and 3's:

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:

Next the property for products:

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.
Next we use the property for powers of the argument:

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:

Combining the like terms we get:

Substituting in the given values:
-(0.431) + 2*(0.683)
0.935

So
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