What is 1/2 log_{10}((y+5)/(y-5)) ?

The solution to 1/2 log_{10}((y+5)/(y-5)) is 1/2 log_{10}(y+5)-1/2 log_{10}(y-5)

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simplify 1/2 log_{10}((y+5)/(y-5))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

9.24 + lo g_{10} (\frac{0.21}{0.24})

lo g_{3} (b) + lo g_{3} (b + 9)

lo g_{10} (\frac{x}{z ^{2}})

- 3 lo g_{10} (z) + 7 lo g_{10} (x) - 5 lo g_{10} (y)

What is 1/2 log_{10}((y+5)/(y-5)) ?
The solution to 1/2 log_{10}((y+5)/(y-5)) is 1/2 log_{10}(y+5)-1/2 log_{10}(y-5)