SOLUTION: how do you condense the following logarithms? I'm confused and need help.
3 log3X + 4 log3Y-4log3Z
and
2[3 ln x-ln(x+1)-ln(x-1)]
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Question 244644: how do you condense the following logarithms? I'm confused and need help.
3 log3X + 4 log3Y-4log3Z
and
2[3 ln x-ln(x+1)-ln(x-1)]
Found 2 solutions by JimboP1977, solver91311:
Answer by JimboP1977(311) (Show Source): You can put this solution on YOUR website!
Log Rules that you should learn:
1)
2)
3)
Assuming log3 means log(base 3):
Using rule 3
Using rule 1 and 2
Using rule 3
Using rule 2
Using rule 3
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ +\ 4\log_3(y)\ -\ 4\log_3(z))
First use:
\ =\ n\log_b(x))
to write:
\ +\ \log_3\left(y^4\right)\ -\ \log_3\left(z^4\right))
Then use the fact that the sum of the logs is the log of the product, that is:
 + \log_b(y) = \log_b(xy))
to write:
\ -\ \log_3\left(z^4\right))
Then use the fact that the difference of the logs is the log of the quotient, that is:
 - \log_b(y) = log_b\left(\frac{x}{y}\right))
To write:
)
and you are done.
\ -\ \ln\left(x-1\right)\right))
Distribute the 2:
\ -\ 2\ln\left(x-1\right))
Then continue in the same fashion as illustrated in the first problem to finish the second one.
John
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