What is log_{10}(x)-3log_{10}(2x)+2log_{10}(4x) ?

The solution to log_{10}(x)-3log_{10}(2x)+2log_{10}(4x) is log_{10}(2)

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simplify log_{10}(x)-3log_{10}(2x)+2log_{10}(4x)

simplify

lo g_{10} (x) - 3 lo g_{10} (2 x) + 2 lo g_{10} (4 x)

lo g_{10} (2)

Decimal Notation

0.30102 \dots

Solution steps

lo g_{10} (x) - 3 lo g_{10} (2 x) + 2 lo g_{10} (4 x)

- 3 lo g_{10} (2 x) = - lo g_{10} ((2 x)^{3})

2 lo g_{10} (4 x) = lo g_{10} ((4 x)^{2})

= lo g_{10} (x) - lo g_{10} ((2 x)^{3}) + lo g_{10} ((4 x)^{2})

Apply log rule:

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

lo g_{10} (x) - lo g_{10} ((2 x)^{3}) = lo g_{10} (\frac{x}{( 2 x ) ^{3}})

= lo g_{10} (\frac{x}{( 2 x ) ^{3}}) + lo g_{10} ((4 x)^{2})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (\frac{x}{( 2 x ) ^{3}}) + lo g_{10} ((4 x)^{2}) = lo g_{10} (\frac{x}{( 2 x ) ^{3}} (4 x)^{2})

= lo g_{10} (\frac{x}{( 2 x ) ^{3}} (4 x)^{2})

Simplify

\frac{x}{( 2 x ) ^{3}} (4 x)^{2} : 2

= lo g_{10} (2)

582 x^{2} - 9 x^{2}

5 c^{1} + 5 c^{3}

\frac{\frac{2}{2}}{x}

2 x^{3} x + 5

(- a + b)^{3}

What is log_{10}(x)-3log_{10}(2x)+2log_{10}(4x) ?
The solution to log_{10}(x)-3log_{10}(2x)+2log_{10}(4x) is log_{10}(2)