Hacker News Reader

Comment by pencil | Hacker News Reader

i completely agree with you sir and i really appologise for not responding to this thread http://news.ycombinator.com/item?id=1107996 to be honest with you i really don't know where i stand .what's my level of competence. i recently gained interest in math and physics because i regret not taking these two subjects seriously back in college.now i work for a bank which pay's peanuts.i don't intend to get a job which helps me build my math/physics skills,i just wanna learn it because i have a burning desire to learn it.it's as simple as that. yes.math requires hours and days of practice which i'am religiously doing but it's not enough for me as it's very evident by the level of knowledge/intellect that i possess. with that being said the number of ways arranging the equation log(x)+3=2t hmm.. log(x)=2t-3 am i right??hope i'am not bullshitting you.

by the way the only definition of logarithm that i know is 'log is inverse of exponents'

View on HN

So what does that mean?

OK, here are some terms to simplify. In each case, what is a simpler way to write the expression:

  x^3 * x^5

  (t^3)^2

  u^(3^2)

Expand the following:

  (g+2)^2

  (z-3)^3

Now, if x=10^y, what does y equal?

now i have the solution for y in x=10^y

here it is:x=10^y

subtract 10^y from both the sides

x-10^y=0

now subtract x from both the sides

-10^y = -x

divide by -1

-10^y/-1 = -x/-1

= 10^y = x

take log base 10 both sides

log10^y = logx

= ylog10=logx

y = logx/log10

Ah, very good. You've gone slightly the long way around, but you've got the right answer.

The first part you go from x=10^y to -10^y=-x to 10^y=x. Is it not clear that if x=10^y then 10^y=x? The point is that any time A=B, then B=A.

Next, you have ended with y=log(x)/log(10). If the logarithms are base 10, what is log(10)? Can you use that to make your result simpler?

Next question: if t=log(u) (where the logarithm is base 10) then what does u equal?

i'am not able to solve t=log(u).not even a single step sorry

i'am assuming this would end up in some number called 'e' which i came accross somewhere in the past.please help..i'am not sure what that number means and how to get it

OK, I really don't know how to help you now using this medium. You claim to have watching the Khan Academy video, but this question is answered in that.

The simple rules are these:

    log(a.b) = log(a) + log(b)

  hence

    log(a^4) = log(a.a.a.a) = log(a)+log(a)+log(a)+log(a) = 4.log(a)

  Therefore

    if  a = b^z
    then log(a) = log(b^z)
    so   log(a) = z.log(b)

This is true for all bases. Then we have

    log_b(b) = 1  :  Log (base b) of b is 1.

    Hence log_b(b^2) = 2
          log_b(b^3) = 3

    and so on.

In all this the basic rule is this:

    if   x = b^y
    then log_b(x) = log_b(b^y)
                  = y.log_b(b)
                  = y

So if the base is 10, then we have:

    If  a = 10^b
    then log(a) = log(10^b)
                = b.log(10)
                = b.1
                = b

So now, start with the equation t=log(u), assuming the log is base 10, and use the above rules to change it around. When you do that, see if you can get to saying u equals something.

Finally, you need to study sections 1, 2 and 3 of this page:

http://en.wikipedia.org/wiki/Logarithm

What's on that page will also help you to understand the questions.

i'll be back in 45 min

x^3+5=x^8

t^3 * t^3 = t^6

i guess it's u^6

g^2+4g+4

not sure abt (z-3)^3

expanding (z-3)^3

could it be: (z-3).(z+3)^2 ??

=>(z-3) (z^2+3z+9)

OK, in the first one you need brackets : x^3+5 is not usually understood to be the same as x^(3+5), but the answer is right, and the process is right. The others are right too.

So (g+2)^2 is equal to g^2+4g+4, but it's also equal to (g+2).(g+2) [where I've used the dot for multiplication]

Does that help you for (z-3)^3 ??

Reply on news.ycombinator.com