5.5 objectives
DESCRIPTION
5.5 Objectives. Apply the base properties of logarithms. Use the change of base formula. Properties of Logarithms. log a 1=0 and log a a =1 log a m+log a n = log a ( mn ) log a m-log a n = log a (m/n) log a ( m r )= rlog a m l n = log e (natural log). Change of base formula. - PowerPoint PPT PresentationTRANSCRIPT
5.5 Objectives
• Apply the base properties of logarithms.• Use the change of base formula.
Properties of Logarithms
1) loga1=0 and logaa=1
2) logam+logan=loga(mn)
3) logam-logan=loga(m/n)
4) loga(mr)=rlogam
ln = loge (natural log)
Change of base formula
• Let x, a, and b be positive numbers..• ..where a≠ 1 and b≠ 1.
logalogx
xlog a
Try these
• ln 5+ ln 4 log 10-log 5
And more…
log 52 log 5 + log 15 – log 10
5.6 Objectives
• Solve exponential equations• Solve logarithmic equations.
Exponential Equations
Basic form: Cax = k1) Solve for ax
2) take the base a log of both sides, which makes the ax equal x because..
logaax = x
3) Solve the other side
Try these
Log (2x+1) =2
Try these
Log2 4x = 2-log2 x
Logarithmic equations
• Basic form: C logax = k.
1) Solve for logax.
2) Exponentiate each side with base a.This makes the logax side equal x because
alogax = x3) Solve.
Try these
log x + log (2x+1) = log 7 2log23x= 1
5.7 Objectives
• Find an exponential model.• Find a logarithmic model.
Types of models
• Exponential– f(x) = Cax
– Can be used to model data that increase or decrease rapidly over time
• Logarithmic– f(x) = a + b log x – Can be used to model data that increase gradually over time
• Logistic– f(x) =– Can be used to model data that at first increase slowly, then
increase rapidly, and finally level of
Exponential model
f(x) = Cax
Logarithmic model
f(x) = a + b log x
Logistic model
assignment
• Page 442-443– 7-14– 31-38
• Page 453– 5-14– 33-38
• Page 462– 1-4