What is 2ln(4)+ln(x+1)-3ln(y) ?

The solution to 2ln(4)+ln(x+1)-3ln(y) is ln((16(x+1))/(y^3))

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simplify 2ln(4)+ln(x+1)-3ln(y)

simplify

2 ln (4) + ln (x + 1) - 3 ln (y)

ln (\frac{16 ( x + 1 )}{y ^{3}})

Solution steps

2 ln (4) + ln (x + 1) - 3 ln (y)

Apply log rule:

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

2 ln (4) = ln (4^{2})

= ln (4^{2}) + ln (x + 1) - 3 ln (y)

Apply log rule:

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

ln (4^{2}) + ln (x + 1) = ln (4^{2} (x + 1))

= ln (4^{2} (x + 1)) - 3 ln (y)

4^{2} = 16

= ln (16 (x + 1)) - 3 ln (y)

Apply log rule:

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

3 ln (y) = ln (y^{3})

= ln (16 (x + 1)) - ln (y^{3})

Apply log rule:

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

ln (16 (x + 1)) - ln (y^{3}) = ln (\frac{16 ( x + 1 )}{y ^{3}})

= ln (\frac{16 ( x + 1 )}{y ^{3}})

- lo g_{10} (1 \times 1 0^{- 9})

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{3} b ^{9}})

lo g_{8} (\frac{5}{x})

16 lo g_{4} (a) - 4 lo g_{4} (b)

lo g_{a} (x^{2} y)

What is 2ln(4)+ln(x+1)-3ln(y) ?
The solution to 2ln(4)+ln(x+1)-3ln(y) is ln((16(x+1))/(y^3))