Logarithmic Functions Mrs. King Pre-Calculus. What are logarithms? The inverse of the exponential function!

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Presentation transcript:

Logarithmic Functions Mrs. King Pre-Calculus

What are logarithms? The inverse of the exponential function!

Graph: Picture from: Regardless of the base, the exponential graph goes through the point (0,1). Therefore, regardless of the base, the logarithmic graph goes through the point (1,0).

Definitions of Logarithms The logarithmic function is the function, where b is any number such that is equivalent to The function is read "log base b of x".

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10 3 = 1000log = = 16log 2 16 = = 10,000log = = 9log 3 9 = = 16log 4 16 = = 0.01log = -2 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / /2 = 6 log 12 1= = 1 log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using exponential notation

The Change of Base Formula

Examples…watch your parenthesis!