What is log_{10}(x)+log_{10}(x^2-25)-log_{10}(8)-log_{10}(x+5) ?

The solution to log_{10}(x)+log_{10}(x^2-25)-log_{10}(8)-log_{10}(x+5) is log_{10}((x(x-5))/8)

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simplify log_{10}(x)+log_{10}(x^2-25)-log_{10}(8)-log_{10}(x+5)

simplify

lo g_{10} (x) + lo g_{10} (x^{2} - 25) - lo g_{10} (8) - lo g_{10} (x + 5)

lo g_{10} (\frac{x ( x - 5 )}{8})

Solution steps

lo g_{10} (x) + lo g_{10} (x^{2} - 25) - lo g_{10} (8) - lo g_{10} (x + 5)

Apply log rule:

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

lo g_{10} (x) + lo g_{10} (x^{2} - 25) = lo g_{10} (x (x^{2} - 25))

= lo g_{10} (x (x^{2} - 25)) - lo g_{10} (8) - lo g_{10} (x + 5)

Apply log rule:

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

lo g_{10} (x (x^{2} - 25)) - lo g_{10} (8) = lo g_{10} (\frac{x ( x ^{2} - 25 )}{8})

= lo g_{10} (\frac{x ( x ^{2} - 25 )}{8}) - lo g_{10} (x + 5)

Apply log rule:

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

lo g_{10} (\frac{x ( x ^{2} - 25 )}{8}) - lo g_{10} (x + 5) = lo g_{10} \frac{\frac{x ( x ^{2} - 25 )}{8}}{x + 5}

= lo g_{10} \frac{\frac{x ( x ^{2} - 25 )}{8}}{x + 5}

Simplify

\frac{\frac{x ( x ^{2} - 25 )}{8}}{x + 5} : \frac{x ( x - 5 )}{8}

= lo g_{10} (\frac{x ( x - 5 )}{8})

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

ln (2 x^{2}) + ln (5 x^{7})

lo g_{10} (y x^{3})

lo g_{10} (x) - lo g_{10} (x + 1)

lo g_{2} (x^{2}) - 3 lo g_{2} (x) - 28

What is log_{10}(x)+log_{10}(x^2-25)-log_{10}(8)-log_{10}(x+5) ?
The solution to log_{10}(x)+log_{10}(x^2-25)-log_{10}(8)-log_{10}(x+5) is log_{10}((x(x-5))/8)