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Popular >

simplify ln((x^θ)^n(θ+1)^n)

Solution

simplify

ln ((x^{θ})^{n} (θ + 1)^{n})

Solution

n ln (x^{θ}) + n ln (θ + 1)

Solution steps

ln ((x^{θ})^{n} (θ + 1)^{n})

Apply log rule:

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

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

= ln ((x^{θ})^{n}) + ln ((θ + 1)^{n})

Apply log rule:

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

ln ((x^{θ})^{n}) = n ln (x^{θ})

= n ln (x^{θ}) + ln ((θ + 1)^{n})

Apply log rule:

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

ln ((θ + 1)^{n}) = n ln (θ + 1)

= n ln (x^{θ}) + n ln (θ + 1)

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expand log_{10}(8x^4)expand

lo g_{10} (8 x^{4})

Frequently Asked Questions (FAQ)

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