AdvAlg9.7LogarithmsToBasesOtherThan10.notebook In order to isolate a variable within a logarithm of an equation, you need to re write the equation as the equivalent exponential equation. In order to isolate a variable that is an exponent of an equation, you need to re write the equation as the equivalent equation using logarithms. Mar 2 8:58 PM 1
The exponential function with base b. If f(x) = log b x then f 1 (x) = b x Mar 2 8:59 PM 2
y=b x The domain is the set of positive real numbers (1, 0) y = log b x The range is the set of all real numbers The x intercept is (1,0); there are no y intercepts The y axis (x=0) is a vertical asymptote to the curve. Mar 2 8:59 PM 3
Logs are exponents! What is the base? raised to what exponent is 9 81 2 Logs are exponents! What is the base? raised to what exponent is 9 27 Logs are exponents! What is the base? raised to what exponent is 9 1 Mar 2 8:59 PM 4
Logarithms are EXPONENTS! Mar 2 9:00 PM 5
Mar 2 9:00 PM 6
Mar 2 9:00 PM 7
In order to isolate a variable within a logarithm of an equation, you need to re write the equation as the equivalent exponential equation. In order to isolate a variable that is an exponent of an equation, you need to re write the equation as the equivalent equation using logarithms. Jan 18 8:55 AM 8
In order to isolate a variable within a logarithm of an equation, you need to re write the equation as the equivalent exponential equation. In order to isolate a variable that is an exponent of an equation, you need to re write the equation as the equivalent equation using logarithms. Jan 18 8:55 AM 9
In order to isolate a variable within a logarithm of an equation, you need to re write the equation as the equivalent exponential equation. In order to isolate a variable that is an exponent of an equation, you need to re write the equation as the equivalent equation using logarithms. Jan 18 8:55 AM 10
See section 9.5 Notes Jan 18 8:55 AM 11
In order to isolate a variable within a logarithm of an equation, you need to re write the equation as the equivalent exponential equation. In order to isolate a variable that is an exponent of an equation, you need to re write the equation as the equivalent equation using logarithms. Jan 18 8:55 AM 12
Mar 2 9:00 PM 13
Mar 2 9:01 PM 14
Mar 2 9:01 PM 15
Mar 2 9:01 PM 16
Mar 2 9:01 PM 17
Mar 2 9:01 PM 18
Mar 2 9:01 PM 19
6 3 =d Mar 6 12:25 PM 20
Mar 6 12:25 PM 21
Mar 2 9:02 PM 22
Mar 2 9:02 PM 23
Mar 2 9:02 PM 24
If log b n = m then log n b = 1/m Mar 2 9:03 PM 25
Mar 2 9:03 PM 26
Mar 6 7:23 AM 27
Mar 5 9:52 AM 28
Mar 2 9:03 PM 29
Feb 26 6:57 PM 30
Mar 6 7:40 AM 31
Mar 2 9:03 PM 32
Feb 26 6:57 PM 33
Mar 2 9:04 PM 34
Mar 2 9:04 PM 35
Mar 2 9:04 PM 36
Mar 2 9:04 PM 37
Mar 2 9:05 PM 38
Mar 6 9:07 AM 39
Mar 6 9:07 AM 40
Mar 8 11:53 AM 41
Mar 6 9:08 AM 42
Mar 6 9:08 AM 43
Mar 6 9:09 AM 44
u 7 y 15 Mar 6 9:10 AM 45
Mar 6 9:03 AM 46
inverse Notes 9 7 y=2 x.125.25.5 1 2 4 8.125.25.5 1 2 4 8 3 2 1 0 1 2 3 All reals y > 0 (pos. reals) x axis (y = 0) (0, 1) None log 2 x = y x > 0 (pos. reals) All reals y axis (x = 0) None (1, 0) Dec 30 8:34 PM 47
base exponent exponent if and only if b n = m answer value exponent answer Dec 30 8:36 PM 48
Dec 30 8:37 PM 49
Dec 30 8:37 PM 50
Dec 30 8:40 PM 51
Dec 30 8:48 PM 52
Apr 14 2:22 PM 53
Mar 2 9:06 PM 54