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

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

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

simplify

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

lo g_{10} (50)

Decimal Notation

1.69897 \dots

Solution steps

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

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

Apply log rule:

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

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

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

2 \cdot 5^{2} = 50

= lo g_{10} (50)

ln (- 2 x)

3 lo g_{10} (6) - 3 lo g_{10} (3)

lo g_{b} (\frac{x ^{2} y}{z ^{7}})

ln (x^{3} + 1) - 2 ln (x - 1)

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