Is the rule log a(x^y) = y log a(x) true?
- Pramod KumarLv 71 month ago
We know that -
logₐ (x)ⁿ = n logₐ (x)
Hence logₐ (xʸ) = y logₐ (x) ............ Hence it's true.
- 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) .
- vaklasLv 41 month ago
Yes, log a(x^y) = y ∙ log a(x) is true. You can find the proof below (y = n)