What is log_{0.5}(x+1)-log_{0.5}(x-3) ?

The solution to log_{0.5}(x+1)-log_{0.5}(x-3) is -log_{2}((x+1)/(x-3))

Popular >

simplify log_{0.5}(x+1)-log_{0.5}(x-3)

simplify

lo g_{0.5} (x + 1) - lo g_{0.5} (x - 3)

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

Solution steps

lo g_{0.5} (x + 1) - lo g_{0.5} (x - 3)

Apply log rule:

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

lo g_{0.5} (x + 1) - lo g_{0.5} (x - 3) = lo g_{0.5} (\frac{x + 1}{x - 3})

= lo g_{0.5} (\frac{x + 1}{x - 3})

Convert

0.5

to a fraction:

\frac{1}{2}

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

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

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

2 lo g_{6} (x - 7) + lo g_{6} (9) - 2

3 lo g_{10} (3) - 3 lo g_{10} (x)

lo g_{b} (15) - 3 lo g_{b} (12)

2 lo g_{10} (5) - 2 lo g_{10} (x)

ln (2 u) - ln (\frac{u}{2})

What is log_{0.5}(x+1)-log_{0.5}(x-3) ?
The solution to log_{0.5}(x+1)-log_{0.5}(x-3) is -log_{2}((x+1)/(x-3))