SOLUTION: Express log3+log2 square root 2-3log 4 as a singular logarithm

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Question 1192977: Express log3+log2 square root 2-3log 4 as a singular logarithm
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Say that differently. As put in the post, it is ambiguous.
If to guess, you are starting with log%28%283%29%29%2Blog%28%282%29%29sqrt%282-3%2Alog%28%284%29%29%29.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note the concept of a "singular logarithm" is not defined....

To write the expression as a SINGLE logarithm, I will assume the expression is

log%28%283%29%29%2Blog%28%282%2Asqrt%282%29%29%29-3%2Alog%28%284%29%29

If that is the correct expression, then use your basic rules of logarithms:

(1) log%28%28A%29%29%2Blog%28%28B%29%29=log%28%28AB%29%29
(2) log%28%28A%29%29-log%28%28B%29%29=log%28%28A%2FB%29%29
(3) n%2Alog%28%28A%29%29=log%28%28A%5En%29%29

Using (1),

Using (3), 3%2Alog%28%284%29%29=log%28%284%5E3%29%29=log%28%2864%29%29

Using (2),

ANSWER: log%28%28%283%2Asqrt%282%29%29%2F32%29%29

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NOTE...!

An answer in unsimplified form is more useful to a student who is just learning about logarithms:

ANSWER: log%28%28%28%283%29%2A%282sqrt%282%29%29%29%2F4%5E3%29%29

In that form you can still see all the parts of the given expression:
The (3) and 2*sqrt(2) are multiplied together; and
that product is divided by 4^3.