What is log_{10}((5x)/3) ?

The solution to log_{10}((5x)/3) is log_{10}(5)+log_{10}(x)-log_{10}(3)

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simplify log_{10}((5x)/3)

simplify

lo g_{10} (\frac{5 x}{3})

lo g_{10} (5) + lo g_{10} (x) - lo g_{10} (3)

Solution steps

lo g_{10} (\frac{5 x}{3})

Apply log rule:

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

lo g_{10} (\frac{5 x}{3}) = lo g_{10} (5 x) - lo g_{10} (3)

= lo g_{10} (5 x) - lo g_{10} (3)

Simplify

lo g_{10} (5 x) : lo g_{10} (5) + lo g_{10} (x)

= lo g_{10} (5) + lo g_{10} (x) - lo g_{10} (3)

2 ln (6 x) - \frac{2}{3} ln (x^{3})

lo g_{4} (5) + lo g_{4} (12) - lo g_{4} (3.75)

lo g_{7} (49 x^{5})

lo g_{\frac{1}{2}} (\frac{2}{3})

lo g_{2} (\frac{y}{8})

What is log_{10}((5x)/3) ?
The solution to log_{10}((5x)/3) is log_{10}(5)+log_{10}(x)-log_{10}(3)