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Question
If log (x + y) = log x + log y, then y is equal to ______.
Options
`x/(x - 1)`
`(x + 1)/x`
`(x - 1)/x`
`x/(x + 1)`
MCQ
Fill in the Blanks
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Solution
If log (x + y) = log x + log y, then y is equal to `underlinebb(x/(x - 1))`.
Explanation:
Use the product rule
log x + log y = log (xy)
So log (x + y) = log (xy)
⇒ x + y = xy (logs defined)
Rearranging gives y(x – 1) = x.
Hence `y = x/(x - 1)`.
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Notes
x and y must be positive logs defined and x ≠ 1.
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