What is ln((3x^{3-1})/(θ^3)) ?

The solution to ln((3x^{3-1})/(θ^3)) is ln(3)+2ln(x)-3ln(θ)

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simplify ln((3x^{3-1})/(θ^3))

simplify

ln (\frac{3 x ^{3 - 1}}{θ ^{3}})

ln (3) + 2 ln (x) - 3 ln (θ)

Solution steps

ln (\frac{3 x ^{3 - 1}}{θ ^{3}})

Apply log rule:

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

ln (\frac{3 x ^{3 - 1}}{θ ^{3}}) = ln (3 x^{3 - 1}) - ln (θ^{3})

= ln (3 x^{3 - 1}) - ln (θ^{3})

Apply log rule:

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

ln (θ^{3}) = 3 ln (θ)

= ln (3 x^{3 - 1}) - 3 ln (θ)

Apply log rule:

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

ln (3 x^{3 - 1}) = ln (3) + ln (x^{3 - 1})

= ln (3) + ln (x^{3 - 1}) - 3 ln (θ)

Apply log rule:

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

ln (x^{3 - 1}) = (3 - 1) ln (x)

= ln (3) + (3 - 1) ln (x) - 3 ln (θ)

Subtract the numbers:

3 - 1 = 2

= ln (3) + 2 ln (x) - 3 ln (θ)

\frac{1}{2} (ln (1 + 2) - ln (- 1 + 2))

2 ln (6) - 3 ln (x)

ln (\frac{a ^{2}}{b ^{- 1} c ^{1}})

\frac{2}{3} \cdot lo g_{10} (7.71 \cdot 1 0^{28}) - 9.1

- lo g_{10} (8.7 \cdot 1 0^{- 12})

What is ln((3x^{3-1})/(θ^3)) ?
The solution to ln((3x^{3-1})/(θ^3)) is ln(3)+2ln(x)-3ln(θ)