Logarithmic Functions Logarithms to other bases log b x a if and only if x b a Note b gt 0 and b 1 The common logarithm of any positive real number ID: 411797
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Slide1
5.5
Logarithmic FunctionsSlide2
Logarithms to other bases
log
b
x = a if and only if x = ba. Note: b > 0, and b ≠ 1The common logarithm of any positive real number x is defined to be the exponent you get when you write x as a power of 10.log x = a IFF x = 10aThis is true because log has a base of 10, however, we do not write it the same way we don’t write x = 1x.For example: log 6.3 ≈ 0.8 because 6.3 ≈ 100.8Slide3
Ex. 1 & 2
Find the decibel level for each sound with the given intensity
I
of an average car at 70 km/h, I = 106.8I0.Find the decibel level of two stereos, playing the same music simultaneously at 62dB.Slide4
Ex. 3 Write each equation in exponential form.
A)
log
4 16 = 2B) log 1000 = 3C)Slide5
Natural Logarithm Function
ln
x = k IFF ek = x**NOTE** The ln eliminates e and vice versaSlide6
Ex. 4 Find the value of x to the nearest hundredth.
A)
10
x = 100 B) ex = 100Slide7
Ex. 5 Find each logarithm. (Do not use a calculator)
A)
log 100
B) log 0.01 C) log3 9D) log5 E) ln e2 F) log5 58Slide8
Ex. 6 Given log 4.17 ≈ 0.6201, find (w/o a
calc
):
HINTSPut given in exp. form & think matchYou can also match and substituteUse properties of logs
A) log 417
log(4.17
10
2
)
log(
10
.6201
10
2
)
log(10
2.6201
)
2.6201
B) log
0.417
4.17
10
.6201
(given
exp. form) (10-1) 4.1710.6201(10-1) .417 10-.3799(matches)log (10-.3799) (plug in) -.3799
C) log log4.17-1 -1log4.17-1(.6201)-.6201
Slide9
Ex. 7 Solve for x
without using a calculator.
A)
log x = 3B) log | x | = 3 C) log | x – 1 | = 3D) log 4 x = 1.5E) ln x = 1.5 F) ln x = 0Slide10
Ex. 8 Solve for x using a calculator.
A)
log
x = 0.7B) ln x = –1.5C) ex = 5