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

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

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

simplify

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

2 lo g_{10} (2)

Decimal Notation

0.60205 \dots

Solution steps

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

Apply log rule:

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

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

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

Cancel

\frac{12 x}{3 x} : 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)

ln (4 h - 8) - ln (4)

\frac{1}{2} ln (x) + 6 ln (y) - 5 ln (z)

- lo g_{10} (4.24 \cdot 1 0^{- 3})

lo g_{10} (y x^{9})

ln (7) + ln (x)

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