What is log_{10}(4)+log_{10}(9) ?

The solution to log_{10}(4)+log_{10}(9) is 2log_{10}(6)

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simplify log_{10}(4)+log_{10}(9)

simplify

lo g_{10} (4) + lo g_{10} (9)

2 lo g_{10} (6)

Decimal Notation

1.55630 \dots

Solution steps

lo g_{10} (4) + lo g_{10} (9)

Apply log rule:

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

lo g_{10} (4) + lo g_{10} (9) = lo g_{10} (4 \cdot 9)

= lo g_{10} (4 \cdot 9)

Multiply the numbers:

4 \cdot 9 = 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} (20 x)

ln (x^{2} 6 - x)

ln (- 5 e^{x})

ln (x (x + 4) (x + 6))

lo g_{10} (7) 7

What is log_{10}(4)+log_{10}(9) ?
The solution to log_{10}(4)+log_{10}(9) is 2log_{10}(6)