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Popular >

simplify ln(Ax^by^c)

Solution

simplify

ln (A x^{b} y^{c})

Solution

ln (A) + b ln (x) + c ln (y)

Solution steps

ln (A x^{b} y^{c})

Apply log rule:

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

ln (A x^{b} y^{c}) = ln (A) + ln (x^{b}) + ln (y^{c})

= ln (A) + ln (x^{b}) + ln (y^{c})

Apply log rule:

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

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

= ln (A) + b ln (x) + ln (y^{c})

Apply log rule:

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

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

= ln (A) + b ln (x) + c ln (y)

Popular Examples

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\frac{97}{100} ln (3 \cdot 1 0^{6}) + \frac{3}{100} ln (3000)

join (sqrt(2)ln((3e^2)/2))/(e)join

\frac{2 ln ( \frac{3 e ^{2}}{2} )}{e}

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4 lo g_{b} (X) - lo g_{b} (y)

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Frequently Asked Questions (FAQ)

What is ln(Ax^by^c) ?
The solution to ln(Ax^by^c) is ln(A)+bln(x)+cln(y)