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

The solution to log_{10}((10x)/3) is 1+log_{10}(x)-log_{10}(3)

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (10 x) : 1 + lo g_{10} (x)

= 1 + lo g_{10} (x) - lo g_{10} (3)

2 lo g_{a} (x) - 4 lo g_{a} (y^{3})

lo g_{9} (9 x^{4}) + lo g_{3} (x)

2 lo g_{10} (8) - 3 lo g_{10} (x)

- \frac{ln ( 3 ) - ln ( 2 )}{ln ( 2 )}

\frac{1}{2} lo g_{10} (x) - 6 lo g_{10} (y)

What is log_{10}((10x)/3) ?
The solution to log_{10}((10x)/3) is 1+log_{10}(x)-log_{10}(3)