SOLUTION: Given logk 3=7, logk 4=13, and logk 5=22, find logk (12/5k^3)^2
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Question 567785: Given logk 3=7, logk 4=13, and logk 5=22, find logk (12/5k^3)^2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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The sum of the logs is the log of the product, the difference of the logs is the log of the quotient, and the log of something to a power is the power times the log:
 + \log_b(y) = \log_b(xy))
 - \log_b(y) = \log_b\left(\frac{x}{y}\right))
\ =\ n\log_b(x))
to write:
^2\ =\ 2\left(\log_k\left(3\right)\ +\ \log\left(4\right)\ -\ \left\[\log_k\left(5\right)\ +\ 3\log_k\left(k\right)\right\]\right))
Then substitute the values you were given plus the fact that \ =\ 1)
to write:
\right\]\right))
And do the arithmetic.
John
My calculator said it, I believe it, that settles it
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