SOLUTION: Given that log 2 ≈ 0.301 and log 3 ≈ 0.477, find the following.
log6 27
Here is the work I have done, can someone check it for me?
log(6) = log(2*3)
log(2) lo
Algebra.Com
Question 270469: Given that log 2 ≈ 0.301 and log 3 ≈ 0.477, find the following.
log6 27
Here is the work I have done, can someone check it for me?
log(6) = log(2*3)
log(2) log(3) = .301 .477 = .778
log6(27) = 1.84
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The key to this problem is to realize that a base 6 logarithm is hard to work with. We need to change the base to one that is easy to work with, like base 10 logarithms. Fortunately there is a formula for doing just this: . Using this formula to change your base 6 logarithm to an expression of base 10 logarithms we get:
We now have base 10 logarithms to work with. Next, since we are given log(2) and log(3), we want to express the arguments in terms of 2's and/or 3's. You already figured out how to express a 6 in terms of 2's and 3's. With a little thought I hope you see that . So rewriting the logarithms using 2's and 3's we get:
Next we can use one property of logarithms, to move the exponent of out in front of the logarithm. And we can use another property of logarithms, , to split the log(2*3) into separate logarithms:
We have finally changed our original base 6 logarithm of 27 into an expression of base 10 logarithms of 2 and 3. We can now use the given values for log(2) and log(3) and simplify:
Rounded to the nearest 1/100 this matches the answer you got. But I have no idea how you came up with this. The work you provided is grossly incomplete.
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