SOLUTION: Express the following as a single logarithm (base is 10 unless otherwise indicated): log2-log3+log5= log2-(log3+log5)= log2-log(3*5)= log2-log15= log(2/5)=0.8751 Now, I d

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Question 1064355: Express the following as a single logarithm (base is 10 unless otherwise indicated):
log2-log3+log5=
log2-(log3+log5)=
log2-log(3*5)=
log2-log15=
log(2/5)=0.8751
Now, I did this problem this way and answers don't match. Please explain why? Thank you very much.
(log2-log3)+log5=
log(2/3)+log5=
log((2/3)*5)=
log(10/3)=0.5228
Now, which one is the solution to the question? I am confused!!!!!!!!!! Thank you very much.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!






As decimal value approximation, 0.52288






-----------Note: in log base 10, .
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Express the following as a single logarithm (base is 10 unless otherwise indicated):
log2-log3+log5=
log2-(log3+log5)=
log2-log(3*5)=
log2-log15=
log(2/5)=0.8751
Now, I did this problem this way and answers don't match. Please explain why? Thank you very much.
(log2-log3)+log5=
log(2/3)+log5=
log((2/3)*5)=
log(10/3)=0.5228
Now, which one is the solution to the question? I am confused!!!!!!!!!! Thank you very much. 
The 2nd simplification is correct.

log 2 - log 3 + log 5 ======>  ======> 

Your 1st simplification was INCORRECT and that's why you got a different answer.

log2 - log 3 + log 5 

log2-(log3+log5) <========= This is INCORRECT

Putting parentheses around the 2nd and 3rd logs in the expression would give you: log 2 - (log 3 - log 5)

I hope you realize that when the OPEN PARENTHESIS is placed around log 3, the "+" after log 3 changes to "-".

Continuing, we get: , which is same as above. 

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