SOLUTION: Write the expression as a single logarithm or single natural logarithm?
1)1/3 log4 27-(2log4 6- 1/2 log4 81)
2)log3 4- log3 2)
3)2ln 8-ln 3+ln x
4)ln a-2ln b+ 1/2 ln c
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Question 583204: Write the expression as a single logarithm or single natural logarithm?
1)1/3 log4 27-(2log4 6- 1/2 log4 81)
2)log3 4- log3 2)
3)2ln 8-ln 3+ln x
4)ln a-2ln b+ 1/2 ln c
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
1) Use
\ =\ n\log_b(x))
to write:
 \LARGE\ -\ \left(\log_4\left(6^2\right)\ -\ \log_4\left(81^{\small{\frac{1}{2}}}\right)\right))
Raise to the indicated powers:
 \LARGE\ -\ \left(\log_4\left(36\right)\ -\ \log_4\left(9\right)\right))
Use "The difference of the logs is the log of the quotient" i.e:
\ -\ \log_b(y)\ =\ \log_b\left(\frac{x}{y}\right))
to write:
\ -\ \log_4\left(\frac{36}{9}\right))
\ -\ \log_4\left(4\right))
)
Done.
John
My calculator said it, I believe it, that settles it
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