What is log_{5}(14x+15)-log_{5}(1/(14x-15)) ?

The solution to log_{5}(14x+15)-log_{5}(1/(14x-15)) is log_{5}((14x+15)(14x-15))

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simplify log_{5}(14x+15)-log_{5}(1/(14x-15))

simplify

lo g_{5} (14 x + 15) - lo g_{5} (\frac{1}{14 x - 15})

lo g_{5} ((14 x + 15) (14 x - 15))

Solution steps

lo g_{5} (14 x + 15) - lo g_{5} (\frac{1}{14 x - 15})

Apply log rule:

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

lo g_{5} (14 x + 15) - lo g_{5} (\frac{1}{14 x - 15}) = lo g_{5} (\frac{14 x + 15}{\frac{1}{14 x - 15}})

= lo g_{5} (\frac{14 x + 15}{\frac{1}{14 x - 15}})

Simplify

\frac{14 x + 15}{\frac{1}{14 x - 15}} : (14 x + 15) (14 x - 15)

= lo g_{5} ((14 x + 15) (14 x - 15))

ln (x^{10} 2 - x)

lo g_{5} (x) - 8 lo g_{5} (y) - 9 lo g_{5} (z)

lo g_{10} (x^{3} y^{6})

lo g_{10} (30) + lo g_{10} (5)

lo g_{x} (\frac{a + 2}{a + 3})

What is log_{5}(14x+15)-log_{5}(1/(14x-15)) ?
The solution to log_{5}(14x+15)-log_{5}(1/(14x-15)) is log_{5}((14x+15)(14x-15))