University:
Glendale Community College
Course:
MAT150 | College Algebra/Functions
Academic year:

2021
Views:

311

Pages:

4
Author:

Kenley Davila

Section 6.5: Properties of Logarithms #1 - 12: Evaluate each expression without a calculator. Check your answer using your calculator. 1) log2 16 This asks the question 2 to what power is 16, 2x = 16) Answer: 4 3) log4 163 I need to rewrite the 16 as 42 Log4(42)3 = log4 46 (this asks 4 to what power is 46 , 4x = 46) Answer: 6 5) log8 85 (this asks 8 to what power is 85, 8x = 85) Answer: 5 7) log3 243 (this asks 3 to what power is 243, 3x = 243) Answer: 5 9) ln(e) Rewrite to loge e (this asks e to what power is e, ex = e) Answer: 1 11) log2 643 (I will change the 64 to 25) Log2(25)3 = log2 215 (this asks 2 to what power is 215, 2x = 215) Answer: 15 #13 – 24: Expand into sums and differences of logarithms (express powers as factors). 13) log3 (x2y3) Write two logs, one for the x the other for the y. put a plus sign between as there is no fraction. Make the powers coefficients Answer: 2log3x + 3log3y 15) log5 (x2y6z) Create 3 logs, one for each letter, no minuses needed as there are no fractions, make powers into coefficients Answer: 2log5 x + 6log5 y + log5 z 17) Create three logs, one for each letter, the log with the z gets a minus in front since the z is in the denominator, make powers into coefficients Answer: log2 x + 3log2 y – 2log2 z 19) Create 4 logs, one for each letter, the logs with the w and z get minuses in front since those letters are in the denominator, make powers into coefficients. Answer: log2 x + log2 y - 2log2 w - 5log2 z 21) log4 (x3y4) Create 2 logs, no minuses needed since no fraction, make powers into coefficients Answer: 3log4x + 4log4y √ 23) Write with fraction exponent ⁄ Create two logs, no minuses as no fractions, make powers into coefficients Answer: #25 - 36: Write the expression as a single logarithm. Write your answer with only positive exponents. 25) 3log2 x + 4log2 y = log2 x3 + log2 y4 Answer = log2 (x3y4) 27) 2log3 x + 4log3 y + log3 z = log3 x2 + log3 y4 + log3 z Answer: log3 (x2y4z) 29) 5log2 x + 3log2 y – log2 z = log2 x5 + log2 y3 – log2 z (the z will go in the denominator because of the minus) Answer: 31) 4log x – 2log y – 3 log z = log x4 – log y2 – log z3 Both y and z will go in denominator because of the minuses Answer: 33) -2log3 x + log3 y + log3 z = log3 y + log3 z – 2log3 x = log3 y + log3 z – log3 x2 Answer: 35) ln x + 3ln y – 2 ln z = ln x + ln y3 – ln z2 Answer: #37 - 45: Use the change of base formula and your calculator to evaluate each logarithm, round your answer to 2 decimal places. 37) log2 3 (log 3 / log 2 on my calculator) Answer: 1.58 39) log 35 (log 5 / log 3 on my calculator) Answer: 1.46 41) log4 0.65 (log 0.65 / log 4 on my calculator) Answer: -.31 43) log5 18 (log 18 / log 5 on my calculator) Answer: 1.80 45) log90.123 (log 0.123 / log 9 on my calculator) Answer: -.95