5.5 objectives

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