How do you write these expressions as single logarithms? 1. 4 log 2 + log 6 2. 3log_2 6-2 3. 5 log 3 - 2 log 8

2 Answers
Feb 17, 2018
  1. log 96
  2. log_2 54
  3. log (243/64)

Explanation:

  1. 4 log 2 + log 6
    to start off, write the expression using exponents.
    log 2^4 + log 6
    since we are adding, we multiply
    log(2^4*6)
    =log(16*6)
    =log 96

  2. 3 log_2 6 - 2
    for this one, we need to make sure the bases are the same so that we are able to combine them.
    log_2 6^3 - log_2 2^2
    since are subtracting, we divide
    log_2(6^3/2^2)
    =log_2(216/4)
    =log_2 54

  3. 5 log 3 - 2 log 8
    log 3^5 - log 8^2
    log(3^5/8^2)
    =log(243/64)

Feb 17, 2018
  1. log(96)
  2. Refer to answer below
  3. log(243/64)

Explanation:

  1. When adding two logs together you multiply
    log(2)+log(6)
    log(2*6)
    If there is a number behind the log it becomes an exponent
    4log(2)+log(6)
    log(2^4*6)
    log(96)

  2. Refer to answer below

  3. When you subtract logs you divide
    5log(3)−2log(8)
    log(3^5/2^8)
    log(243/64)