SOLUTION: CHallenge: Under Certain conditions, the wind speed s (in knots) at an altitude of h meters above a grassy plain can be modeled by this function: s(h)=2 ln (100h

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: CHallenge: Under Certain conditions, the wind speed s (in knots) at an altitude of h meters above a grassy plain can be modeled by this function: s(h)=2 ln (100h      Log On

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Question 197635This question is from textbook Texas Edition McDougal Littell Algebra 2
: CHallenge: Under Certain conditions, the wind speed s (in knots) at an altitude of h meters above a grassy plain can be modeled by this function:
s(h)=2 ln (100h)
a. By what amount does the wind speed increase when the altitude doubles
b. Show that the given function can be written in terms of common logarithms as s(h)=2/loge (log h+2)
umm on a , so far I got change in altitude=s(2h)-s(h)
then 2ln(100(2h))-2ln(100h) then idk
on b, i'm not quite sure what to do, This question is from textbook Texas Edition McDougal Littell Algebra 2

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
a)

s%28h%29=2%2Aln%28100h%29 Start with the given equation.


s%282h%29=2%2Aln%28100%282h%29%29 Replace "h" with "2h" (since the altitude doubles)


s%282h%29=2%2Aln%282%2A100h%29 Rearrange the terms.


s%282h%29=2%28ln%282%29%2Bln%28100h%29%29 Expand the log using the identity ln%28A%2AB%29=ln%28A%29%2Bln%28B%29


s%282h%29=2%2Aln%282%29%2B2%2Aln%28100h%29 Distribute


s%282h%29=2%2Aln%282%29%2Bs%28h%29 Replace 2%2Aln%28100h%29 with s%28h%29. Note: this can be done since s%28h%29=2%2Aln%28100h%29


s%282h%29=ln%282%5E2%29%2Bs%28h%29 Rewrite the log using the identity y%2Aln%28x%29=ln%28x%5Ey%29


s%282h%29=ln%284%29%2Bs%28h%29 Square 2 to get 4


So when the altitude doubles, the speed of the wind increases by ln%284%29 knots. Since , this means that the speed of the wind increases by about 1.38629 knots.


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b)

Are you only supposed to convert to a common log? If so, then there's not much to this part...


s%28h%29=2%2Aln%28100h%29 Start with the given equation.


s%28h%29=2%2Alog%28e%2C%28100h%29%29 Convert to a standard log of base "e"


s%28h%29=2%2A%28log%2810%2C%28100h%29%29%2Flog%2810%2C%28e%29%29%29 Now use the change of base formula (this step may be optional)


Remember the change of base formula is log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29