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

The solution to 2log_{10}(5)+log_{10}(4)-log_{10}(2) is log_{10}(50)

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

simplify

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

lo g_{10} (50)

Decimal Notation

1.69897 \dots

Solution steps

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

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

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

Add similar elements:

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

= 2 lo g_{10} (5) + lo g_{10} (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5^{2} \cdot 2 = 50

= lo g_{10} (50)

3 lo g_{b} (m) - 2 lo g_{b} (n)

lo g_{10} (x - 1) + lo g_{10} (x + 1)

lo g_{10} (\frac{x ^{5}}{y ^{2}})

ln (e (x + 5))

ln (\frac{e ^{4}}{9})

What is 2log_{10}(5)+log_{10}(4)-log_{10}(2) ?
The solution to 2log_{10}(5)+log_{10}(4)-log_{10}(2) is log_{10}(50)