What is log_{10}(2)+log_{10}(18) ?

The solution to log_{10}(2)+log_{10}(18) is 2log_{10}(6)

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simplify log_{10}(2)+log_{10}(18)

simplify

lo g_{10} (2) + lo g_{10} (18)

2 lo g_{10} (6)

Decimal Notation

1.55630 \dots

Solution steps

lo g_{10} (2) + lo g_{10} (18)

Apply log rule:

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

lo g_{10} (2) + lo g_{10} (18) = lo g_{10} (2 \cdot 18)

= lo g_{10} (2 \cdot 18)

Multiply the numbers:

2 \cdot 18 = 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} (y^{8} z)

lo g_{3} (4) + 2 lo g_{3} (\frac{1}{2}) + lo g_{3} (x)

lo g_{10} (3 x + 1) - lo g_{10} (3 x^{2} - 5 x - 2)

ln (2 e^{1})

lo g_{6} (\frac{w ^{5}}{v})

What is log_{10}(2)+log_{10}(18) ?
The solution to log_{10}(2)+log_{10}(18) is 2log_{10}(6)