Question 287937
You are given expressions to use for log(2) and log(3). And you should know that log(10) = 1 by definition. So your task is to express log(200) in terms of these three.<br>
There are three properties we can use:<ul><li>The log of a product: {{{log(a, (p*q)) = log(a, (p)) + log(a, (q))}}}</li><li>The log of a quotient: {{{log(a, (p/q)) = log(a, (p)) - log(a, (q))}}}</li>The log of an exponentiated expression: {{{log(a, (p^q)) = q*log(a, (p))}}}</li></ul>
So with these properties, if we can express 200 as a product, quotient and/or power of 2's, 3's and/or 10's we will have able to solve the problem. With the 0's at the end of 200 I hope you can see that a product of 10's in involved and with the 2 in front we can see that a 2 is involved:
log(200) = log(2*10*20) = log(2) + log(10) + log(10) = a + 1 + 1 = a + 2