What is log_{10}((x^2-c^2)/2)-log_{10}(x-c) ?

The solution to log_{10}((x^2-c^2)/2)-log_{10}(x-c) is log_{10}((x+c)/2)

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simplify log_{10}((x^2-c^2)/2)-log_{10}(x-c)

simplify

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

lo g_{10} (\frac{x + c}{2})

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{x ^{2} - c ^{2}}{2}) - lo g_{10} (x - c) = lo g_{10} (\frac{\frac{x ^{2} - c ^{2}}{2}}{x - c})

= lo g_{10} (\frac{\frac{x ^{2} - c ^{2}}{2}}{x - c})

Simplify

\frac{\frac{x ^{2} - c ^{2}}{2}}{x - c} : \frac{x + c}{2}

= lo g_{10} (\frac{x + c}{2})

2 ln (3) - \frac{1}{2} ln (2) + \frac{π}{12}

lo g_{10} (\frac{x ^{2}}{7})

lo g_{5} (\frac{25}{x + 5})

lo g_{2} (\frac{3 y}{z})

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

What is log_{10}((x^2-c^2)/2)-log_{10}(x-c) ?
The solution to log_{10}((x^2-c^2)/2)-log_{10}(x-c) is log_{10}((x+c)/2)