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Popular >

simplify ln((θ+1)^n*(x^θ))

Solution

simplify

ln ((θ + 1)^{n} \cdot (x^{θ}))

Solution

n ln (θ + 1) + θ ln (x)

Solution steps

ln ((θ + 1)^{n} (x^{θ}))

Apply log rule:

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

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

= ln ((θ + 1)^{n}) + ln (x^{θ})

Apply log rule:

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

ln ((θ + 1)^{n}) = n ln (θ + 1)

= n ln (θ + 1) + ln (x^{θ})

Apply log rule:

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

ln (x^{θ}) = θ ln (x)

= n ln (θ + 1) + θ ln (x)

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Frequently Asked Questions (FAQ)

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