What is 3ln(x-6)-10ln(x) ?

The solution to 3ln(x-6)-10ln(x) is ln(((x-6)^3)/(x^{10)})

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simplify 3ln(x-6)-10ln(x)

simplify

3 ln (x - 6) - 10 ln (x)

ln (\frac{( x - 6 ) ^{3}}{x ^{10}})

Solution steps

3 ln (x - 6) - 10 ln (x)

Apply log rule:

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

3 ln (x - 6) = ln ((x - 6)^{3})

= ln ((x - 6)^{3}) - 10 ln (x)

Apply log rule:

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

10 ln (x) = ln (x^{10})

= ln ((x - 6)^{3}) - ln (x^{10})

Apply log rule:

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

ln ((x - 6)^{3}) - ln (x^{10}) = ln (\frac{( x - 6 ) ^{3}}{x ^{10}})

= ln (\frac{( x - 6 ) ^{3}}{x ^{10}})

ln (x + 2) + ln (x^{2} - 1)

ln \frac{( ( tan ( x ) ) ^{4} )}{e ^{4 x^{4}} x ^{7}}

ln (\frac{100.2}{100})

0.23 \cdot ln (0.23) + 5.55 ln (0.76)

What is 3ln(x-6)-10ln(x) ?
The solution to 3ln(x-6)-10ln(x) is ln(((x-6)^3)/(x^{10)})