We did a quiz and a couple of questions here's the answers in a more detailed explanation:
For this question, you can think of log 2000 as log (2 x 1000). Then knowing that logs are exponents, we know that when exponents are being multiplied they're really being added together, therefore we get log 2 + log 1000. The value of log 2 is already given as 0.301 and the value of log 1000 is 3 because 10^3 is 1000. Add the two numbers together and you get 3.301, the closest answer to this value would be B).
In log 8 we can change the 8 to 2^3 because that's equivalent to 8. Then since 3 is an exponent we can take it out and put it in front of log so it looks like 3log 2. We know the value of log 2 which is 0.301. Multiply it by 3 and you get 0.903. Closest answer to that is C).
There's actually two ways you can come about to answer this question. First way, you know that log 2 = 0.301. With that you can take the reciprocal and punch it into your calculator to give you an answer around 3. Then there's the much easier way of just finding values for x in 2^x that would give you an answer closest to log2 (1o), which would be 3, that answer is C).
The first one basically explains itself so I'll move onto the next one. This is basically just like the first one however there's an extra step to finding the answers. You must first factor the 4 as an exponent which gives you 2². since the exponent 2 and the log are both exponents you can place the 2 as an exponent of 3. This allows the two bases of 2 cancel out along with the log which leaves you with 3² which gives you 9 as an answer.
To find the answer to this question you change both logarithms into exponents which gives you 3^k = 10 and 9^x = 10. Then in order to solve for x you must make the bases of each exponent the same, we do this by changing 9 to 3² which is the exponential equivalent to 9. Now since we have the same bases all we need to do is solve for the exponential part of the power which gives us x = k/2. That would be answer C).
We had a Pre-test on Logs & Exponents, here's the answers in more detailed explanations:
.........ok nevermind, the blog is refusing to let me upload my pictures onto this post therefore I can't provide you with questions and detailed explanations, this will have to wait even longer now, I'm sorry but this WOULD'VE been done tonight if it weren't for this DAMN glitch, my apologies again.
SCRIBE FOR TOMORROW IS JENG!