What is log_{10}((2x)/5) ?

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

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simplify log_{10}((2x)/5)

simplify

lo g_{10} (\frac{2 x}{5})

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

Solution steps

lo g_{10} (\frac{2 x}{5})

Apply log rule:

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

lo g_{10} (\frac{2 x}{5}) = lo g_{10} (2 x) - lo g_{10} (5)

= lo g_{10} (2 x) - lo g_{10} (5)

Simplify

lo g_{10} (2 x) : lo g_{10} (2) + lo g_{10} (x)

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

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

lo g_{3} (x + 25) - lo g_{3} (x - 1)

lo g_{4} (x^{2} - 4) - 6 lo g_{4} (x + 2)

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

\frac{1}{6} ln (y) + ln (z)

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