SOLUTION: Hi, Can you help me with this math problem? 19.) Rewrite the expression as a single logarithm. 2 log4 (2x+3)+3 log4 (4x+4) The answer should be log4(2x+3)^2(4x+4)^

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hi, Can you help me with this math problem? 19.) Rewrite the expression as a single logarithm. 2 log4 (2x+3)+3 log4 (4x+4) The answer should be log4(2x+3)^2(4x+4)^      Log On


   

Question 135804: Hi,
Can you help me with this math problem?
19.) Rewrite the expression as a single logarithm.
2 log4 (2x+3)+3 log4 (4x+4)
The answer should be log4(2x+3)^2(4x+4)^3
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is based on one rule. It is:
log%28a%2Cb%29+%2B+log%28a%2Cc%29+%2B+log%28a%2Cd%29+=+log%28a%2Cbcd%29
You can verify it with numbers
log%282%2C4%29+%2B+log%282%2C8%29+%2B+log%282%2C16%29+=+log%282%2C4%2A8%2A16%29
2+%2B+3+%2B+4+=+log%282%2C512%29
9+=+log%282%2C512%29
2%5E9+=+512
512+=+512
---------------------------
2%2Alog%284%2C%282x%2B3%29%29+%2B+3%2Alog%284%2C%284x%2B4%29%29
This can be rewritten as:

Following the above rule,
log%284%2C%282x%2B3%29%282x%2B3%29%29+%2B+log%284%2C%284x%2B4%29%284x%2B4%29%284x%2B4%29%29
log%284%2C%282x%2B3%29%5E2%29+%2B+log%284%2C%284x%2B4%29%5E3%29
Now apply the rule one more time
log%284%2C%282x%2B3%29%5E2%2A%284x%2B4%29%5E3%29 answer