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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{2} = 4

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

Apply log rule:

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

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

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

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lo g_{10} (1024) - 3 lo g_{10} (2) - lo g_{10} (3)

lo g_{10} (t^{3})

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