What is log_{5}(x-1)+log_{5}(x-2)-log_{5}(x+6) ?

The solution to log_{5}(x-1)+log_{5}(x-2)-log_{5}(x+6) is log_{5}(((x-1)(x-2))/(x+6))

Popular >

simplify log_{5}(x-1)+log_{5}(x-2)-log_{5}(x+6)

simplify

lo g_{5} (x - 1) + lo g_{5} (x - 2) - lo g_{5} (x + 6)

lo g_{5} (\frac{( x - 1 ) ( x - 2 )}{x + 6})

Solution steps

lo g_{5} (x - 1) + lo g_{5} (x - 2) - lo g_{5} (x + 6)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{5} (x - 1) + lo g_{5} (x - 2) = lo g_{5} ((x - 1) (x - 2))

= lo g_{5} ((x - 1) (x - 2)) - lo g_{5} (x + 6)

Apply log rule:

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

lo g_{5} ((x - 1) (x - 2)) - lo g_{5} (x + 6) = lo g_{5} (\frac{( x - 1 ) ( x - 2 )}{x + 6})

= lo g_{5} (\frac{( x - 1 ) ( x - 2 )}{x + 6})

4 lo g_{7} (x) - 2 lo g_{7} (y) - 2 lo g_{7} (z)

lo g_{10} (3 x) + 7

2 (lo g_{7} (x) + 2 lo g_{7} (y) - 3 lo g_{7} (z))

\frac{1}{2} lo g_{10} (\frac{y + 5}{y - 5})

3 ln (x) - 2 ln (2 x)

What is log_{5}(x-1)+log_{5}(x-2)-log_{5}(x+6) ?
The solution to log_{5}(x-1)+log_{5}(x-2)-log_{5}(x+6) is log_{5}(((x-1)(x-2))/(x+6))