What is 9x+3ln(x-1)-3ln(2)+4ln(x) ?

The solution to 9x+3ln(x-1)-3ln(2)+4ln(x) is 9x+ln((x^4(x-1)^3)/8)

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simplify 9x+3ln(x-1)-3ln(2)+4ln(x)

simplify

9 x + 3 ln (x - 1) - 3 ln (2) + 4 ln (x)

9 x + ln (\frac{x ^{4} ( x - 1 ) ^{3}}{8})

Solution steps

9 x + 3 ln (x - 1) - 3 ln (2) + 4 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= 9 x + ln ((x - 1)^{3}) - 3 ln (2) + 4 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (2) = ln (2^{3})

= 9 x + ln ((x - 1)^{3}) - ln (2^{3}) + 4 ln (x)

Apply log rule:

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

ln ((x - 1)^{3}) - ln (2^{3}) = ln (\frac{( x - 1 ) ^{3}}{2 ^{3}})

= 9 x + ln (\frac{( x - 1 ) ^{3}}{2 ^{3}}) + 4 ln (x)

2^{3} = 8

= 9 x + ln (\frac{( x - 1 ) ^{3}}{8}) + 4 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (x) = ln (x^{4})

= 9 x + ln (\frac{( x - 1 ) ^{3}}{8}) + ln (x^{4})

Apply log rule:

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

ln (\frac{( x - 1 ) ^{3}}{8}) + ln (x^{4}) = ln (x^{4} \frac{( x - 1 ) ^{3}}{8})

= 9 x + ln (x^{4} \frac{( x - 1 ) ^{3}}{8})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 9 x + ln (\frac{x ^{4} ( x - 1 ) ^{3}}{8})

- 3 ln ∣ x + 3 ∣ + 3 ln ∣ x + 1 ∣

\frac{1}{2} \cdot ln (\frac{0.697}{0.1828})

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

ln (\frac{1}{35.2 - 1})

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

What is 9x+3ln(x-1)-3ln(2)+4ln(x) ?
The solution to 9x+3ln(x-1)-3ln(2)+4ln(x) is 9x+ln((x^4(x-1)^3)/8)