generis wrote:
dave13 wrote:
generis please tell me if my solution is correct, i got 9 but negative 9
where am i wrong . . .
\(0.05^{m-k}\) =\(5*10^7\) now i need to convert this
\(5*10^7\) into 0.05 to have the same base
\(0.05^{m-k}\) =
\(0.05^{-9}\) now equate bases
\(m-k\) =\(-9\)
dave13 Wow - SO close.
Your arithmetic is hard! Despite that degree of difficulty, you had everything correct until the highlight.
Please show me your steps?How did you get from
\(5 * 10^7\) to \(.05 * 10^{-9}\)?
dave13 wrote:
generis great to hear from you
many thanks for your question
i am happy to respond
\(5 * 10^7\) to \(.05 * 10^{-9}\)?
\(5 * 10^7\) means 5+7 zeros --> 50 000 000 so now i need to get 0.05 so i move 9 decimal points left
if i am doing something wrong here \(0.05^{m-k}\) = \(0.05^{-9}\) - than how to equate bases?
dave13 - Whoops! Opposite direction. Now I see what happened.
You say that
\(.05 * 10^{-9} = 50,000,000\)But if I move 9 decimal digits to the left, with 50,000,000, I get
.050000000. That is not correct. LHS now = .05 (that's all - zeros to right of 5 don't matter)
In fact,
\(.05 * 10^{-9}= .000000005\)It's an easy and common mistake.
We need to ask, how do I write .05 so that it equals 50,000,000?
(.05 times WHAT = 50,000,000?)
\(.05 * x = 50,000,000?\)
.05: as abhimahna mentions, move the decimal 9 places to the right = 50,000,000, so
RHS:\(.05 * 10^9 = 50,000,000\)
I'm going back to this formulation of yours for LHS:
\(\frac{0.015*10^m}{0.3*10^k}\)
Divide decimals first, then 10s.
\(\frac{.015}{.3} =.05\)
\(\frac{10^m}{10^k} = 10^{m-k}\)
LHS altogether is
\(.05 * 10^{m-k}\)So now you have
\(0.05 * 10 ^{m-k}\) = \(0 .05 * 10^9\)
\(m - k = 9\)I have an idea that might work better.
Try to change things into
integer bases. JMO, but it's easier.
So when you get to
\(.05 * 10^{(m-k)}\)Use
powers of 10 to change .05 to 5, so that LHS (5) = RHS(5)
\(.05 = 5 * 10^{-2}\)Whole thing now is:
\(5 * 10^{-2} * 10^{(m-k)} = 5 * 10^7\)Consolidate powers of 10 on LHS
Thus:
\(5 * 10^{(m-k-2)} = 5 * 10^7\) Now equate powers of 10 . . . see what you get.
Convert bases to integers, IMO. It's easier to keep track of direction.
You did just fine.