What is expand log_{3}(243(x-1)^4) ?

The solution to expand log_{3}(243(x-1)^4) is 5+4log_{3}(x-1)

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expand log_{3}(243(x-1)^4)

expand

lo g_{3} (243 (x - 1)^{4})

5 + 4 lo g_{3} (x - 1)

Solution steps

lo g_{3} (243 (x - 1)^{4})

Apply log rule:

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

lo g_{3} (243 (x - 1)^{4}) = lo g_{3} (243) + lo g_{3} ((x - 1)^{4})

= lo g_{3} (243) + lo g_{3} ((x - 1)^{4})

Apply log rule:

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

lo g_{3} ((x - 1)^{4}) = 4 lo g_{3} (x - 1)

= lo g_{3} (243) + 4 lo g_{3} (x - 1)

lo g_{3} (243) = 5

= 5 + 4 lo g_{3} (x - 1)

2 lo g_{b} (z) - lo g_{b} (y)

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

- lo g_{10} (4.1 x 1 0^{- 4})

- ln (\frac{5}{3})

\frac{ln ( 2 ) + ln ( 3 )}{2}

What is expand log_{3}(243(x-1)^4) ?
The solution to expand log_{3}(243(x-1)^4) is 5+4log_{3}(x-1)