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

The solution to 2log_{10}(3)+log_{10}(4) is 2log_{10}(6)

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

simplify

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

2 lo g_{10} (6)

Decimal Notation

1.55630 \dots

Solution steps

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

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

Apply log rule:

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

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

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

3^{2} \cdot 4 = 36

= lo g_{10} (36)

Factor the number:

36 = 6^{2}

= lo g_{10} (6^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (6^{2}) = 2 lo g_{10} (6)

= 2 lo g_{10} (6)

lo g_{10} (\frac{z ^{3}}{y x ^{5}})

lo g_{b} (\frac{8}{7})

lo g_{10} (2) - lo g_{10} (0.2)

2 ln (x) - \frac{1}{8} ln (y)

5 \cdot lo g_{10} (a) + \frac{1}{2} \cdot lo g_{10} (b) - 4 \cdot lo g_{10} (c)

What is 2log_{10}(3)+log_{10}(4) ?
The solution to 2log_{10}(3)+log_{10}(4) is 2log_{10}(6)