What is log_{a}(7)+log_{a}(x-1)-log_{a}(x) ?

The solution to log_{a}(7)+log_{a}(x-1)-log_{a}(x) is log_{a}((7(x-1))/x)

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simplify log_{a}(7)+log_{a}(x-1)-log_{a}(x)

simplify

lo g_{a} (7) + lo g_{a} (x - 1) - lo g_{a} (x)

lo g_{a} (\frac{7 ( x - 1 )}{x})

Solution steps

lo g_{a} (7) + lo g_{a} (x - 1) - lo g_{a} (x)

Apply log rule:

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

lo g_{a} (7) + lo g_{a} (x - 1) = lo g_{a} (7 (x - 1))

= lo g_{a} (7 (x - 1)) - lo g_{a} (x)

Apply log rule:

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

lo g_{a} (7 (x - 1)) - lo g_{a} (x) = lo g_{a} (\frac{7 ( x - 1 )}{x})

= lo g_{a} (\frac{7 ( x - 1 )}{x})

3 (lo g_{6} (x) + 3 lo g_{6} (y) - 4 lo g_{6} (z))

- \frac{1}{2} - ln (\frac{1}{3})

ln (4 x^{2}) + ln (3 x^{2})

lo g_{10} (\frac{3 x}{4 y ^{2}})

lo g_{4} (3) + 5 lo g_{4} (y)

What is log_{a}(7)+log_{a}(x-1)-log_{a}(x) ?
The solution to log_{a}(7)+log_{a}(x-1)-log_{a}(x) is log_{a}((7(x-1))/x)