SOLUTION: Write the expression as the sum or difference of single logarithms x and y
log^7 (2x/7)
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Question 242511: Write the expression as the sum or difference of single logarithms x and y
log^7 (2x/7)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I sincerely hope you meant:
)
rather than:
)
which is what you actually wrote.
Going with my initial assumption:
The difference of the logs is the log of the quotient:
 - \log_b(y) = \log_b\left(\frac{x}{y}\right))
So:
\ =\ \log_7\left(2x\right)\ -\ \log_7\left(7\right))
The sum of the logs is the log of the product:
 + \log_b(y) = \log_b(xy))
\ -\ \log_7\left(7\right)\ =\ \log_7\left(x\right)\ +\ \log_7\left(2\right)\ -\ \log_7\left(7\right))
The log to the base b of b is 1:
So:
\ +\ \log_7\left(2\right)\ -\ \log_7\left(7\right)\ =\ \log_7\left(x\right)\ +\ \log_7\left(2\right)\ -\ 1)
John
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