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

The solution to log_{10}((4x)/5) is 2log_{10}(2)+log_{10}(x)-log_{10}(5)

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simplify log_{10}((4x)/5)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (4 x) : 2 lo g_{10} (2) + lo g_{10} (x)

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

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

ln (\frac{e ^{9}}{5})

lo g_{3} (6 c) + lo g_{3} (\frac{1}{12})

- \frac{1}{45} ln (\frac{18 - ( - 7 )}{22 - ( - 7 )})

6000 ln (100) - 6000 ln (50)

What is log_{10}((4x)/5) ?
The solution to log_{10}((4x)/5) is 2log_{10}(2)+log_{10}(x)-log_{10}(5)