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

The solution to log_{10}(3)+2log_{10}(2) is log_{10}(12)

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

simplify

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

lo g_{10} (12)

Decimal Notation

1.07918 \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} (x y)

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

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

3 \cdot 2^{2} = 12

= lo g_{10} (12)

3 lo g_{10} (a) + 5 lo g_{10} (b) - lo g_{10} (ab)

lo g_{10} (5 \cdot 2)

lo g_{5} (\frac{x}{3 ^{2} z})

ln (e^{3 x}) + ln (x^{3}) - ln (3 x)

ln (25 e^{2} \cdot \frac{1}{36})

What is log_{10}(3)+2log_{10}(2) ?
The solution to log_{10}(3)+2log_{10}(2) is log_{10}(12)