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

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

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simplify log_{10}(3)-2log_{10}(2)

simplify

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

lo g_{10} (\frac{3}{4})

Decimal Notation

- 0.12493 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{2} = 4

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

lo g_{3} (405) + lo g_{3} (5)

ln (\frac{1}{2} e^{x})

3 \cdot lo g_{2} (3) - 2 lo g_{2} (5)

lo g_{3} (x + 2) + lo g_{3} (5)

ln (9 x^{2})

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