What is log_{10}(12)-log_{10}(3) ?

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

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simplify log_{10}(12)-log_{10}(3)

simplify

lo g_{10} (12) - lo g_{10} (3)

2 lo g_{10} (2)

Decimal Notation

0.60205 \dots

Solution steps

lo g_{10} (12) - lo g_{10} (3)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (12) - lo g_{10} (3) = lo g_{10} (\frac{12}{3})

= lo g_{10} (\frac{12}{3})

Divide the numbers:

\frac{12}{3} = 4

= lo g_{10} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= 2 lo g_{10} (2)

lo g_{7} (\frac{7}{y})

ln (a + b) + ln (a - b) - 3 ln (c)

lo g_{3} (10 x) - lo g_{3} (2)

ln (2 x^{2})

lo g_{4} (12 \cdot 3)

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