What is log_{10}(16x^2)+2log_{10}(1/x) ?

The solution to log_{10}(16x^2)+2log_{10}(1/x) is 4log_{10}(2)

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simplify log_{10}(16x^2)+2log_{10}(1/x)

simplify

lo g_{10} (16 x^{2}) + 2 lo g_{10} (\frac{1}{x})

4 lo g_{10} (2)

Decimal Notation

1.20411 \dots

Solution steps

lo g_{10} (16 x^{2}) + 2 lo g_{10} (\frac{1}{x})

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

2 lo g_{10} (\frac{1}{x}) = lo g_{10} ((\frac{1}{x})^{2})

= lo g_{10} (16 x^{2}) + lo g_{10} ((\frac{1}{x})^{2})

Apply log rule:

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

lo g_{10} (16 x^{2}) + lo g_{10} ((\frac{1}{x})^{2}) = lo g_{10} (16 x^{2} (\frac{1}{x})^{2})

= lo g_{10} (16 x^{2} (\frac{1}{x})^{2})

Simplify

16 x^{2} (\frac{1}{x})^{2} : 16

= lo g_{10} (16)

Factor the number:

16 = 2^{4}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 4 lo g_{10} (2)

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

lo g_{b} (\frac{7}{9})

lo g_{10} (8) + lo g_{10} (x)

ln (\frac{5}{100})

lo g_{10} (lo g_{10} (10000 0^{200 x}))

What is log_{10}(16x^2)+2log_{10}(1/x) ?
The solution to log_{10}(16x^2)+2log_{10}(1/x) is 4log_{10}(2)