What is log_{4}(x^2-25)-log_{4}(x-5) ?

The solution to log_{4}(x^2-25)-log_{4}(x-5) is log_{4}(x+5)

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simplify log_{4}(x^2-25)-log_{4}(x-5)

simplify

lo g_{4} (x^{2} - 25) - lo g_{4} (x - 5)

lo g_{4} (x + 5)

Solution steps

lo g_{4} (x^{2} - 25) - lo g_{4} (x - 5)

Apply log rule:

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

lo g_{4} (x^{2} - 25) - lo g_{4} (x - 5) = lo g_{4} (\frac{x ^{2} - 25}{x - 5})

= lo g_{4} (\frac{x ^{2} - 25}{x - 5})

Simplify

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

= lo g_{4} (x + 5)

lo g_{10} (x) - 5 lo g_{10} (y) + 7 lo g_{10} (z)

- [- \frac{3}{10} ln (3) + \frac{8}{35} ln (8) + \frac{15}{14} ln (1)]

lo g_{10} (x^{2} - 7 x - 8) - lo g_{10} (x^{2} - 1)

ln (\frac{( c ^{1 - n} m ^{n} ) ^{1 - l}}{1 - l})

20 lo g_{10} (2) + 40 lo g_{10} (0.04)

What is log_{4}(x^2-25)-log_{4}(x-5) ?
The solution to log_{4}(x^2-25)-log_{4}(x-5) is log_{4}(x+5)