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Lecture Comments (1)

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Post by Akeel Howell on June 18, 2015

How do logarithms relate to taking derivatives and integrals?

Logarithmic Functions

  • and

Logarithmic Functions

Given y = log1234567(541), find 1234567y
  • y = log1234567(541)
  • 1234567y = 1234567log1234567(541)
  • 1234567y = 541
1234567y = 541
Solve for x, ln(x3) = 1
  • ln(x3) = 1
  • 3ln(x) = 1
  • ln(x) = [1/3]
  • eln(x) = e[1/3]
  • x = e[1/3]
x = e[1/3]
Simplify logb(25) − logb(24)
logb(25) − logb(24) = logb([(25)/(24)]) = logb(2)
Solve for x, x = logy(y)
  • x = logy(y)
  • yx = ylogy(y)
  • yx = y = y1
x = 1
Solve for y, ln([x/y]) = 0
  • ln([x/y]) = 0
  • ln(x) − ln(y) = 0
  • ln(x) = ln(y)
  • eln(x) = eln(y)
  • x = y
y = x
Solve for x, log2(x2) − log2(x[1/3]) = 8
  • log2(x) − log2(x[1/3]) = 8
  • log2([x/(x[1/3])]) = 8
  • log2(x1 − [1/3]) = 8
  • log2(x[2/3]) = 8
  • [2/3]log2(x) = 8
  • log2(x) = 12
  • x = 212 = 4096
4096
Solve for x, x = log1234567(1)log(99999999999999)
  • logb (1) = 0
x = log1234567(1)log(99999999999999) = 0 * log(99999999999999) = 0
Simplify eln(x) + 2
eln(x) + 2 = eln(x)e2 = x(e2)
Here, the base is irrelevant. logb(1) = 0
Solve for x, ln(x + 8) + ln(x) − ln(9) = 0
  • ln(x + 8) + ln(x) − ln(9) = 0
  • ln([((x + 8) x)/9]) = 0
  • ln([(x2 + 8x)/9]) = 0
  • [(x2 + 8x)/9] = e0
  • [(x2 + 8x)/9] = 1
  • x2 + 8x = 9
  • x2 + 8x − 9 = 0
  • v(x + 9) (x − 1) = 0
  • x = 1, −9
  • The second solution, -9, would be outside of the domain of lnx. For lnx, x must be greater than 0. So x = 1
x = 1
Prove logb(x) = [(loga(x))/(logb(x))]
  • Let y = logb(x) and z = loga(x)
  • y = logb(x)
  • by = x
  • z = loga(x)
  • z = loga(by)
  • z = yloga(b)
  • z = logb(x)loga(b)
  • loga(x) = logb(x)loga(b)
  • logb(x) = [(loga(x))/(loga(b))]
logb(x) = [(loga(x))/(loga(b))]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Logarithmic Functions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Types of Functions: Logarithmic 0:06
    • General Form
    • 2 Special Logarithmic Func.
    • Euler's # / Natural Log
  • Logarithmic & Exponential Relationship 0:45
    • Log form
  • Properties 2:09
  • Example 1: Apply Basic Principle of Log Func. 3:05
  • Example 2: Use Properties 3:40
  • Example 3: Regular Log 5:16