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

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(35256) (Show Source): You can put this solution on YOUR website!
a)

Start with the given equation.

Replace "h" with "2h" (since the altitude doubles)

Rearrange the terms.

Expand the log using the identity

Distribute

Replace with . Note: this can be done since

Rewrite the log using the identity

Square 2 to get 4

So when the altitude doubles, the speed of the wind increases by 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...

Start with the given equation.

Convert to a standard log of base "e"

Now use the change of base formula (this step may be optional)

Remember the change of base formula is

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