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Popular >

simplify ln(1/(θ^n))

Solution

simplify

ln (\frac{1}{θ ^{n}})

Solution

- n ln (θ)

Solution steps

ln (\frac{1}{θ ^{n}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{θ ^{n}}) = ln (1) - ln (θ^{n})

= ln (1) - ln (θ^{n})

Apply log rule:

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

ln (θ^{n}) = n ln (θ)

= ln (1) - n ln (θ)

Apply log rule:

lo g_{a} (1) = 0

= 0 - n ln (θ)

0 - n ln (θ) = - n ln (θ)

= - n ln (θ)

Popular Examples

simplify-1/2 log_{2}(2sqrt(x))simplify

- \frac{1}{2} lo g_{2} (2 x)

simplify log_{10}(100*a)simplify

lo g_{10} (100 \cdot a)

simplify 1/2 ln(17/15)simplify

\frac{1}{2} ln (\frac{17}{15})

simplify 1/2 [ln(x-4)+5ln(x^2+4x)]simplify

\frac{1}{2} [ln (x - 4) + 5 ln (x^{2} + 4 x)]

simplify log_{10}(2x)+log_{10}(8x)simplify

lo g_{10} (2 x) + lo g_{10} (8 x)

Frequently Asked Questions (FAQ)

What is ln(1/(θ^n)) ?
The solution to ln(1/(θ^n)) is -nln(θ)