What is log_{9}(2x+3)-log_{9}(1/(2x-3)) ?

The solution to log_{9}(2x+3)-log_{9}(1/(2x-3)) is log_{9}((2x+3)(2x-3))

Popular >

simplify log_{9}(2x+3)-log_{9}(1/(2x-3))

simplify

lo g_{9} (2 x + 3) - lo g_{9} (\frac{1}{2 x - 3})

lo g_{9} ((2 x + 3) (2 x - 3))

Solution steps

lo g_{9} (2 x + 3) - lo g_{9} (\frac{1}{2 x - 3})

Apply log rule:

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

lo g_{9} (2 x + 3) - lo g_{9} (\frac{1}{2 x - 3}) = lo g_{9} (\frac{2 x + 3}{\frac{1}{2 x - 3}})

= lo g_{9} (\frac{2 x + 3}{\frac{1}{2 x - 3}})

Simplify

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

= lo g_{9} ((2 x + 3) (2 x - 3))

lo g_{10} (x^{2} + x + 1) + lo g_{10} (x - 1)

lo g_{10} (x^{2} - 16) - 2 lo g_{10} (x + 4)

2 lo g_{10} (x) + 3 lo g_{10} (x + 1)

\frac{1}{3} lo g_{10} (a) - \frac{2}{5} lo g_{10} (b)

lo g_{10} (2) + lo g_{10} (3) - lo g_{10} (5)

What is log_{9}(2x+3)-log_{9}(1/(2x-3)) ?
The solution to log_{9}(2x+3)-log_{9}(1/(2x-3)) is log_{9}((2x+3)(2x-3))