What is ((1))/((2)(log_{5)(x-8)-log_{5}(x))} ?

The solution to ((1))/((2)(log_{5)(x-8)-log_{5}(x))} is 1/(2log_{5)((x-8)/x)}

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simplify ((1))/((2)(log_{5)(x-8)-log_{5}(x))}

simplify

\frac{( 1 )}{( 2 ) ( lo g _{5} ( x - 8 ) - lo g _{5} ( x ) )}

\frac{1}{2 lo g _{5} ( \frac{x - 8}{x} )}

Solution steps

\frac{1}{( 2 ) ( lo g _{5} ( x - 8 ) - lo g _{5} ( x ) )}

Apply rule:

(a) = a

(2) = 2

= \frac{1}{2 ( lo g _{5} ( x - 8 ) - lo g _{5} ( x ) )}

Apply log rule:

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

lo g_{5} (x - 8) - lo g_{5} (x) = lo g_{5} (\frac{x - 8}{x})

= \frac{1}{2 lo g _{5} ( \frac{x - 8}{x} )}

lo g_{2} (\frac{9}{8})

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

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}})

What is ((1))/((2)(log_{5)(x-8)-log_{5}(x))} ?
The solution to ((1))/((2)(log_{5)(x-8)-log_{5}(x))} is 1/(2log_{5)((x-8)/x)}