What is log_{b}(x)+log_{b}(x+6)-log_{b}(24) ?

The solution to log_{b}(x)+log_{b}(x+6)-log_{b}(24) is log_{b}((x(x+6))/(24))

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simplify log_{b}(x)+log_{b}(x+6)-log_{b}(24)

simplify

lo g_{b} (x) + lo g_{b} (x + 6) - lo g_{b} (24)

lo g_{b} (\frac{x ( x + 6 )}{24})

Solution steps

lo g_{b} (x) + lo g_{b} (x + 6) - lo g_{b} (24)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{b} (x) + lo g_{b} (x + 6) = lo g_{b} (x (x + 6))

= lo g_{b} (x (x + 6)) - lo g_{b} (24)

Apply log rule:

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

lo g_{b} (x (x + 6)) - lo g_{b} (24) = lo g_{b} (\frac{x ( x + 6 )}{24})

= lo g_{b} (\frac{x ( x + 6 )}{24})

ln (\frac{x - 1}{x})

lo g_{10} (3) + lo g_{10} (x - 8)

2 [ln (x) + \frac{1}{4} ln (x + 9)]

lo g_{10} (3) + lo g_{10} (x - 4)

lo g_{10} (x^{\frac{1}{2}} (x + 1)^{3})

What is log_{b}(x)+log_{b}(x+6)-log_{b}(24) ?
The solution to log_{b}(x)+log_{b}(x+6)-log_{b}(24) is log_{b}((x(x+6))/(24))