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
log 96 log_2 54 log (243/64)
Explanation:
-
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 -
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 -
5 log 3 - 2 log 8
log 3^5 - log 8^2
log(3^5/8^2)
=log(243/64)
Feb 17, 2018
log(96) - Refer to answer below
log(243/64)
Explanation:
-
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) -
Refer to answer below
-
When you subtract logs you divide
5log(3)−2log(8)
log(3^5/2^8)
log(243/64)