Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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

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  • 1 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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  • 1 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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  • vaklas
    Lv 4
    1 month ago

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

    Attachment image
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