Aim: How do we use logarithms to find values of products and quotients?
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Aim: Log Products & Quotients Course: Alg. 2 & Trig. Aim: How do we use logarithms to find values of products and quotients? Do Now: Evaluate to prove or disprove: log (4.5 + 16) or log 20.5 = log 4.5 + log 16 log (4.5 16) = log 4.5 + log 16 log (4.5 16) = log 4.5 - log 16 log (4.5 16 ) = 16 log 4.5
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Aim: How do we use logarithms to find values of products and quotients?. Do Now:. Evaluate to prove or disprove: log (4.5 + 16) or log 20.5 = log 4.5 + log 16 log (4.5 16) = log 4.5 + log 16 log (4.5 16) = log 4.5 - log 16 log (4.5 16 ) = 16 log 4.5. - PowerPoint PPT Presentation
Transcript of Aim: How do we use logarithms to find values of products and quotients?
Aim: Log Products & Quotients Course: Alg. 2 & Trig.
Aim: How do we use logarithms to find values of products and quotients?
Do Now:
Evaluate to prove or disprove:
log (4.5 + 16) or log 20.5 = log 4.5 + log 16
log (4.5 16) = log 4.5 + log 16
log (4.5 16) = log 4.5 - log 16
log (4.516) = 16 log 4.5
Aim: Log Products & Quotients Course: Alg. 2 & Trig.
Properties of Logarithms
For any positive numbers M, N, and b, b 1,Each of the following statements is true.
logb MN = logb M + logb N Product Property
logb M/N = logb M – logb N Quotient Property
logb Mk = k logb M Power Property
log (3 • 5) = log 3 + log 5
log (3 / 5) = log 3 – log 5
log 35 = 5 log 3
Note: loga(M + N) ≠ loga M + loga N
Note: base must be the same
Aim: Log Products & Quotients Course: Alg. 2 & Trig.
Model Problems
Write each log expression as a single logarithm
a. log3 20 – log3 4
b. 3 log2 x + log2 y
c. log 8 – 2 log 2 + log 3
Expand each log expression
d. log5 x/y
e. log 3r4
Quotient Property3 3
20= log log 5
4
Power and Product Properties
3 32 2 2= log + log logx y x y
Quotient, Power and Product Properties
= log6 .77815...
= log5 x – log5 y
= log 3 + 4 log r
Aim: Log Products & Quotients Course: Alg. 2 & Trig.
Model Problems
Rewrite log 7x3
Expand log2 3xy2
Condense log 2 - 2log x
Express in terms of log m and log n
logm
n3
log 7 + 3 log x
log2 3 + log2 x + 2log2 y
2
2log
x
1 1 1log log (log log )
3 3 3m n m n
Aim: Log Products & Quotients Course: Alg. 2 & Trig.
Model Problems
Given ln 2 0.693, ln 3 1.099, and ln 7 1.946, use the properties of logs to approximate a) ln 6 b) ln 7/27
ln 6 = ln (2 • 3) = ln 2 + ln 3
0.693 + 1.099 1.792
= ln 7 – ln 27
= ln 7 – 3 ln 3 1.946 – 3(1.099) -1.351
ln 7/27
Aim: Log Products & Quotients Course: Alg. 2 & Trig.
Model Problems
Use properties of logarithms to rewrite
ln3x 5
7
as the sum and/or difference of logs
ln3x 5
7 = ln(3x – 5)1/2 – ln 7
= 1/2 ln(3x – 5) – ln 7
Rewrite the following as a single quantity
1/2 log10x – 3 log10(x + 1)
= log10x1/2 – log10(x + 1)3 =
log10
x
(x 1)3
