What is 3log_{10}(5)+2log_{10}(3)-4log_{10}(2) ?

The solution to 3log_{10}(5)+2log_{10}(3)-4log_{10}(2) is log_{10}(1125/16)

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simplify 3log_{10}(5)+2log_{10}(3)-4log_{10}(2)

simplify

3 lo g_{10} (5) + 2 lo g_{10} (3) - 4 lo g_{10} (2)

lo g_{10} (\frac{1125}{16})

Decimal Notation

1.84703 \dots

Solution steps

3 lo g_{10} (5) + 2 lo g_{10} (3) - 4 lo g_{10} (2)

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

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

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

= lo g_{10} (5^{3}) + lo g_{10} (3^{2}) - lo g_{10} (2^{4})

Apply log rule:

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

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

= lo g_{10} (5^{3} \cdot 3^{2}) - lo g_{10} (2^{4})

Apply log rule:

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

lo g_{10} (5^{3} \cdot 3^{2}) - lo g_{10} (2^{4}) = lo g_{10} (\frac{5 ^{3} \cdot 3 ^{2}}{2 ^{4}})

= lo g_{10} (\frac{5 ^{3} \cdot 3 ^{2}}{2 ^{4}})

\frac{5 ^{3} \cdot 3 ^{2}}{2 ^{4}} = \frac{1125}{16}

= lo g_{10} (\frac{1125}{16})

- lo g_{10} (4 \cdot 1 0^{- 4})

lo g_{10} (\frac{5 a ^{2} b ^{4} c}{2 x y})

lo g_{9} (81 x^{8})

- lo g_{10} (5 \cdot 1 0^{- 2})

What is 3log_{10}(5)+2log_{10}(3)-4log_{10}(2) ?
The solution to 3log_{10}(5)+2log_{10}(3)-4log_{10}(2) is log_{10}(1125/16)