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Popular >

simplify ln(sx^ay^b)

Solution

simplify

ln (s x^{a} y^{b})

Solution

ln (s) + a ln (x) + b ln (y)

Solution steps

ln (s x^{a} y^{b})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (s x^{a} y^{b}) = ln (s) + ln (x^{a}) + ln (y^{b})

= ln (s) + ln (x^{a}) + ln (y^{b})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{a}) = a ln (x)

= ln (s) + a ln (x) + ln (y^{b})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (y^{b}) = b ln (y)

= ln (s) + a ln (x) + b ln (y)

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Frequently Asked Questions (FAQ)

What is ln(sx^ay^b) ?
The solution to ln(sx^ay^b) is ln(s)+aln(x)+bln(y)