What is log_{10}(5)-2log_{10}(3) ?

The solution to log_{10}(5)-2log_{10}(3) is log_{10}(5/9)

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simplify log_{10}(5)-2log_{10}(3)

simplify

lo g_{10} (5) - 2 lo g_{10} (3)

lo g_{10} (\frac{5}{9})

Decimal Notation

- 0.25527 \dots

Solution steps

lo g_{10} (5) - 2 lo g_{10} (3)

Apply log rule:

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

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

= lo g_{10} (5) - lo g_{10} (3^{2})

Apply log rule:

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

lo g_{10} (5) - lo g_{10} (3^{2}) = lo g_{10} (\frac{5}{3 ^{2}})

= lo g_{10} (\frac{5}{3 ^{2}})

3^{2} = 9

= lo g_{10} (\frac{5}{9})

0.6 lo g_{2} (0.6) + 0.4 lo g_{2} (0.4)

lo g_{10} (25) + lo g_{10} (4) + lo g_{10} (2)

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

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

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

What is log_{10}(5)-2log_{10}(3) ?
The solution to log_{10}(5)-2log_{10}(3) is log_{10}(5/9)