What is 0.5log_{b}(x+7)-log_{b}(x-3) ?

The solution to 0.5log_{b}(x+7)-log_{b}(x-3) is log_{b}(((x+7)^{0.5})/(x-3))

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simplify 0.5log_{b}(x+7)-log_{b}(x-3)

simplify

0.5 lo g_{b} (x + 7) - lo g_{b} (x - 3)

lo g_{b} (\frac{( x + 7 ) ^{0.5}}{x - 3})

Solution steps

0.5 lo g_{b} (x + 7) - lo g_{b} (x - 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.5 lo g_{b} (x + 7) = lo g_{b} ((x + 7)^{0.5})

= lo g_{b} ((x + 7)^{0.5}) - lo g_{b} (x - 3)

Apply log rule:

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

lo g_{b} ((x + 7)^{0.5}) - lo g_{b} (x - 3) = lo g_{b} (\frac{( x + 7 ) ^{0.5}}{x - 3})

= lo g_{b} (\frac{( x + 7 ) ^{0.5}}{x - 3})

- lo g_{10} (1.6 x 1 0^{- 4})

ln (y^{2} + 5) - ln (y^{2} - 2)

lo g_{6} (\frac{1}{120})

x + ln (x) + ln (2)

\frac{ln ( x ) - ln ( 3 )}{x - 3}

What is 0.5log_{b}(x+7)-log_{b}(x-3) ?
The solution to 0.5log_{b}(x+7)-log_{b}(x-3) is log_{b}(((x+7)^{0.5})/(x-3))