What is ln(x-6)-ln(x-2)+10ln(x) ?

The solution to ln(x-6)-ln(x-2)+10ln(x) is ln((x^{10}(x-6))/(x-2))

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simplify ln(x-6)-ln(x-2)+10ln(x)

simplify

ln (x - 6) - ln (x - 2) + 10 ln (x)

ln (\frac{x ^{10} ( x - 6 )}{x - 2})

Solution steps

ln (x - 6) - ln (x - 2) + 10 ln (x)

Apply log rule:

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

ln (x - 6) - ln (x - 2) = ln (\frac{x - 6}{x - 2})

= ln (\frac{x - 6}{x - 2}) + 10 ln (x)

Apply log rule:

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

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

= ln (\frac{x - 6}{x - 2}) + ln (x^{10})

Apply log rule:

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

ln (\frac{x - 6}{x - 2}) + ln (x^{10}) = ln (\frac{x - 6}{x - 2} x^{10})

= ln (\frac{x - 6}{x - 2} x^{10})

Multiply fractions:

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

= ln (\frac{x ^{10} ( x - 6 )}{x - 2})

6 ln (\frac{1}{2})

ln (\frac{16}{15})

ln (64) + ln (7) - 5 ln (2)

- ln (75) - 3 ln (\frac{15}{22})

ln (0.3 e^{4})

What is ln(x-6)-ln(x-2)+10ln(x) ?
The solution to ln(x-6)-ln(x-2)+10ln(x) is ln((x^{10}(x-6))/(x-2))