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

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

Popular >

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

simplify

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

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

Solution steps

\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})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Apply rule:

1 \cdot a = a

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

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

lo g_{4} (\frac{x ^{2}}{5})

lo g_{10} (1 x)

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27)

lo g_{7} ((\frac{x}{y})^{2})

lo g_{10} (\frac{2 a ^{2}}{3})

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