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# Is the rule log a(x^y) = y log a(x) true?

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- Pramod KumarLv 71 month ago
We know that -

logₐ (x)ⁿ = n logₐ (x)

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Hence logₐ (xʸ) = y logₐ (x) ............ Hence it's true.

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- Keith ALv 61 month ago
log (a * x^y)

= log a + log (x^y) -- product rule

= log a + y * log x -- power rule,

which ts not equal to y log (a*x) .

(There is another problem here: what is the significance of a (.) ? Is a a function; or do the parentheses merely represent multiplication?)

Edit: I see now that the intention is log to base a -- in which case, spacing is a problem; and a better notation would be log_a (x^y) .

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- vaklasLv 41 month ago
Yes, log a(x^y) = y ∙ log a(x) is true. You can find the proof below (y = n)

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