What is 2ln(x)+ln(x-4)-ln(y) ?

The solution to 2ln(x)+ln(x-4)-ln(y) is ln((x^2(x-4))/y)

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simplify 2ln(x)+ln(x-4)-ln(y)

simplify

2 ln (x) + ln (x - 4) - ln (y)

ln (\frac{x ^{2} ( x - 4 )}{y})

Solution steps

2 ln (x) + ln (x - 4) - ln (y)

Apply log rule:

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

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

= ln (x^{2}) + ln (x - 4) - ln (y)

Apply log rule:

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

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

= ln (x^{2} (x - 4)) - ln (y)

Apply log rule:

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

ln (x^{2} (x - 4)) - ln (y) = ln (\frac{x ^{2} ( x - 4 )}{y})

= ln (\frac{x ^{2} ( x - 4 )}{y})

ln (\frac{40}{6})

\frac{ln ( - 0.1 ) - ln ( 5 )}{x - 5}

ln (8) - 2 ln (6) + ln (18)

lo g_{7} (3 x^{2}) - e^{3 x - 6}

ln (\frac{λ}{2 π})

What is 2ln(x)+ln(x-4)-ln(y) ?
The solution to 2ln(x)+ln(x-4)-ln(y) is ln((x^2(x-4))/y)