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Popular >

simplify ln(a^pib^pi)

Solution

simplify

ln (a^{π} b^{π})

Solution

π ln (a) + π ln (b)

Solution steps

ln (a^{π} b^{π})

Apply log rule:

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

ln (a^{π} b^{π}) = ln (a^{π}) + ln (b^{π})

= ln (a^{π}) + ln (b^{π})

Apply log rule:

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

ln (a^{π}) = π ln (a)

= π ln (a) + ln (b^{π})

Apply log rule:

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

ln (b^{π}) = π ln (b)

= π ln (a) + π ln (b)

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Frequently Asked Questions (FAQ)

What is ln(a^pib^pi) ?
The solution to ln(a^pib^pi) is piln(a)+piln(b)