What is ln(x-6)-2ln(x+2)+5ln(x) ?

The solution to ln(x-6)-2ln(x+2)+5ln(x) is ln((x^5(x-6))/((x+2)^2))

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simplify ln(x-6)-2ln(x+2)+5ln(x)

simplify

ln (x - 6) - 2 ln (x + 2) + 5 ln (x)

ln (\frac{x ^{5} ( x - 6 )}{( x + 2 ) ^{2}})

Solution steps

ln (x - 6) - 2 ln (x + 2) + 5 ln (x)

Apply log rule:

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

2 ln (x + 2) = ln ((x + 2)^{2})

= ln (x - 6) - ln ((x + 2)^{2}) + 5 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)^{2}) = ln (\frac{x - 6}{( x + 2 ) ^{2}})

= ln (\frac{x - 6}{( x + 2 ) ^{2}}) + 5 ln (x)

Apply log rule:

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

5 ln (x) = ln (x^{5})

= ln (\frac{x - 6}{( x + 2 ) ^{2}}) + ln (x^{5})

Apply log rule:

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

ln (\frac{x - 6}{( x + 2 ) ^{2}}) + ln (x^{5}) = ln (\frac{x - 6}{( x + 2 ) ^{2}} x^{5})

= ln (\frac{x - 6}{( x + 2 ) ^{2}} x^{5})

Multiply fractions:

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

= ln (\frac{x ^{5} ( x - 6 )}{( x + 2 ) ^{2}})

ln (\frac{72}{100})

ln (\frac{500}{x ^{6}})

ln (\frac{1}{1 - x}) \cdot e

ln (3) + ln (2 x)

6 lo g_{5} (x) - 6 lo g_{5} (y)

What is ln(x-6)-2ln(x+2)+5ln(x) ?
The solution to ln(x-6)-2ln(x+2)+5ln(x) is ln((x^5(x-6))/((x+2)^2))