What is 1/2 x-5+3ln(x-1)-3ln(x-2) ?

The solution to 1/2 x-5+3ln(x-1)-3ln(x-2) is x/2-5+ln(((x-1)^3)/((x-2)^3))

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simplify 1/2 x-5+3ln(x-1)-3ln(x-2)

simplify

\frac{1}{2} x - 5 + 3 ln (x - 1) - 3 ln (x - 2)

\frac{x}{2} - 5 + ln (\frac{( x - 1 ) ^{3}}{( x - 2 ) ^{3}})

Solution steps

\frac{1}{2} x - 5 + 3 ln (x - 1) - 3 ln (x - 2)

Apply log rule:

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

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

= \frac{1}{2} x - 5 + ln ((x - 1)^{3}) - 3 ln (x - 2)

Apply log rule:

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

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

= \frac{1}{2} x - 5 + ln ((x - 1)^{3}) - ln ((x - 2)^{3})

Apply log rule:

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

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

= \frac{1}{2} x - 5 + ln (\frac{( x - 1 ) ^{3}}{( x - 2 ) ^{3}})

\frac{1}{2} x = \frac{x}{2}

= \frac{x}{2} - 5 + ln (\frac{( x - 1 ) ^{3}}{( x - 2 ) ^{3}})

ln (\frac{1200}{400})

ln (\frac{2}{y - 2})

ln (\frac{50 \cdot 12}{70.5 \cdot 8.9})

ln (\frac{573.15 x}{293.15 x})

lo g_{10} (y^{9} x)

What is 1/2 x-5+3ln(x-1)-3ln(x-2) ?
The solution to 1/2 x-5+3ln(x-1)-3ln(x-2) is x/2-5+ln(((x-1)^3)/((x-2)^3))