What is log_{5}((9x^2-y^2)/(2(3x+y))) ?

The solution to log_{5}((9x^2-y^2)/(2(3x+y))) is log_{5}(3x-y)-log_{5}(2)

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simplify log_{5}((9x^2-y^2)/(2(3x+y)))

simplify

lo g_{5} (\frac{9 x ^{2} - y ^{2}}{2 ( 3 x + y )})

lo g_{5} (3 x - y) - lo g_{5} (2)

Solution steps

lo g_{5} (\frac{9 x ^{2} - y ^{2}}{2 ( 3 x + y )})

Simplify

\frac{9 x ^{2} - y ^{2}}{2 ( 3 x + y )} : \frac{3 x - y}{2}

= lo g_{5} (\frac{3 x - y}{2})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{5} (\frac{3 x - y}{2}) = lo g_{5} (3 x - y) - lo g_{5} (2)

= lo g_{5} (3 x - y) - lo g_{5} (2)

lo g_{10} (lo g_{10} (n) - lo g_{10} (49))

2 lo g_{a} (z + 1) + lo g_{a} (3 z + 2)

ln (\frac{x - 3}{e ^{x}})

ln (9) + \frac{1}{2} ln (x + 4) - 5 ln (1 + x)

lo g_{10} (x + 5) - lo g_{10} (x^{2} + 9 x + 20)

What is log_{5}((9x^2-y^2)/(2(3x+y))) ?
The solution to log_{5}((9x^2-y^2)/(2(3x+y))) is log_{5}(3x-y)-log_{5}(2)