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

The solution to 1/(3(ln(y)-2ln(x+y))) is 1/(3ln(\frac{y){(x+y)^2})}

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

simplify

\frac{1}{3 ( ln ( y ) - 2 ln ( x + y ) )}

\frac{1}{3 ln ( \frac{y}{( x + y ) ^{2}} )}

Solution steps

\frac{1}{3 ( ln ( y ) - 2 ln ( x + y ) )}

Apply log rule:

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

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

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

Apply log rule:

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

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

= \frac{1}{3 ln ( \frac{y}{( x + y ) ^{2}} )}

3 lo g_{10} (x) + 2 lo g_{10} (y - 4)

- \frac{5 ln ( 20 )}{ln ( 2 )}

ln (x^{5}) - 2 ln (x^{3})

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

lo g_{10} (2 \cdot 1 0^{- 3})

What is 1/(3(ln(y)-2ln(x+y))) ?
The solution to 1/(3(ln(y)-2ln(x+y))) is 1/(3ln(\frac{y){(x+y)^2})}