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

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

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

simplify

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

ln (\frac{( x + 1 ) ^{4}}{y ^{3}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (\frac{( x + 1 ) ^{4}}{y ^{3}})

ln (\frac{x ^{2} - 4 x + 3}{x ^{2} - 5 x + 6})

- \frac{9}{14} \cdot lo g_{2} (\frac{9}{14}) - \frac{5}{14} \cdot lo g_{2} (\frac{5}{14})

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

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