I slept through all unit..I dunno how to do..things x_x I don't even know how to do 4^x = 64, by hand. I just went 4x4x4 until I got 64 X_x SIGHHHHHH. Don't get logs What if I wanna solve something like.. Logx X^z and what if there are square roots like.. log 5 square root 5
Let me explain it in terms of Loga b = ? What's being asked is a to the power of WHAT (as in the question mark) is b. a^? = b So in your Logx X ^ z question What's being asked is... x^? = x^z ?=z Z is the answer. Whenever it's Loga a^b, the answer is always b. The log base a of a always cancels out.
For: Logx X^z Basically the small x here is the base, and the big X is the value, when you have both the base and value as the same number or variable, you get the answer "1". For e.g. Log of base 10 and value 10 is 1, or Log of base 25 and value 25 is 1, or Log of base x and value x is 1, etc. When you see that the value has a power sign (X^z for instance), you can change it to: Which means you multiply z and Logx X. It is just one of the rules of Log that you have to remember. Since you know that Logx X is 1, then z * 1 will give you z. Answer = z For this, always remember that you have to convert the value to an actual whole number. Square root actually means to the power of half. Which means square root 5 is actually 5^1/2. So your question becomes Log5 5^1/2. If you have read what I mentioned above, then this should be pretty easy. Basically you move the power to the front again, so you get: Code (Text): (1/2)Log5 5 And since you know Log5 5 is actually 1. Then your answer will be (1/2)(1) which is 1/2. Answer = 1/2 Hope that helped. EDIT: By the way, don't worry about the part where 4^x is 64 and you aren't sure of the value of x. There is a way to solve it via log, but most people would just calculate it manually. With practise you should be able to get it quickly, usually what I do is I estimate the value of x, for this case x shouldn't be too big, so it's probably up to a maximum of 4-5, then just trial and error from there.
this is why I'm glad that by next week friday, I will be done math forever good luck with this though, it all seems simple until the test, then they'll throw some crazy stuff at you