What is log_{10}(4x+5)-log_{10}(x) ?

The solution to log_{10}(4x+5)-log_{10}(x) is log_{10}((4x+5)/x)

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simplify log_{10}(4x+5)-log_{10}(x)

simplify

lo g_{10} (4 x + 5) - lo g_{10} (x)

lo g_{10} (\frac{4 x + 5}{x})

Solution steps

lo g_{10} (4 x + 5) - lo g_{10} (x)

Apply log rule:

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

lo g_{10} (4 x + 5) - lo g_{10} (x) = lo g_{10} (\frac{4 x + 5}{x})

= lo g_{10} (\frac{4 x + 5}{x})

lo g_{10} (\frac{2}{y})

lo g_{10} (x \cdot y)

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

ln (x) + ln (7)

lo g_{2} (\frac{8 x ^{2}}{y}) - 2 lo g_{2} (2 x^{2} y)

What is log_{10}(4x+5)-log_{10}(x) ?
The solution to log_{10}(4x+5)-log_{10}(x) is log_{10}((4x+5)/x)