University:
Campbell University
Course:
MATH 111 | College Algebra
Academic year:

2022
Views:

188

Pages:

1
Author:

Emilee Weeks

Logarithm Rules Conversion To convert between the exponential and the logarithmic forms transfer corresponding elements from one to the other. Exponents: Base Exponent Logarithm: Log Base (Result)  Exponent  Result Example: Base = 5 5  25 2 Log 5 (25)  2 Exponent = 2 Result = 25 Trick: Follow the arrow and rewrite elements in the new order. Rewrite b then y then x. Log b x   y  by  x bx  y Log b y   x  Properties For the general case where the letters m, n and b are positive numbers. 1. Log b ( b)  1 Example: 2. Log b (1)  0 Example: Log 5 5  1 Log 5 1  0 3. Log b (m  n)  Log b (m)  Log b (n) --- Log to base ‘b’ of ‘b’ = 1. --- Log to any base of 1 = 0. --- Product Property Example: Log10 (4  x)  Log10 (4)  Log10 ( x) m 4. Log b    Log b (m)  Log b (n) --- Quotient Property n 6 Example: Log10    Log10 (6)  Log10 ( z ) z p 5. Log b r   p  Log b r  --- Power Property Example: Log10 x 2   2  Log10 x  Log x  Ln x  6. Log a x   Log a  Ln a  Log x  Example: Log 5 x   Log5 --- Change of base Caution! The ‘result’ in the logarithm can never be negative; Log 5 (25) is NOT valid.