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Popular >

simplify ln(θ^n*x^{θ-1})

Solution

simplify

ln (θ^{n} \cdot x^{θ - 1})

Solution

n ln (θ) + (θ - 1) ln (x)

Solution steps

ln (θ^{n} x^{θ - 1})

Apply log rule:

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

ln (θ^{n} x^{θ - 1}) = ln (θ^{n}) + ln (x^{θ - 1})

= ln (θ^{n}) + ln (x^{θ - 1})

Apply log rule:

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

ln (θ^{n}) = n ln (θ)

= n ln (θ) + ln (x^{θ - 1})

Apply log rule:

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

ln (x^{θ - 1}) = (θ - 1) ln (x)

= n ln (θ) + (θ - 1) ln (x)

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Frequently Asked Questions (FAQ)

What is ln(θ^n*x^{θ-1}) ?
The solution to ln(θ^n*x^{θ-1}) is nln(θ)+(θ-1)ln(x)