What is log_{10}(12x^4)-log_{10}(4x) ?

The solution to log_{10}(12x^4)-log_{10}(4x) is log_{10}(3x^3)

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simplify log_{10}(12x^4)-log_{10}(4x)

simplify

lo g_{10} (12 x^{4}) - lo g_{10} (4 x)

lo g_{10} (3 x^{3})

Solution steps

lo g_{10} (12 x^{4}) - lo g_{10} (4 x)

Apply log rule:

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

lo g_{10} (12 x^{4}) - lo g_{10} (4 x) = lo g_{10} (\frac{12 x ^{4}}{4 x})

= lo g_{10} (\frac{12 x ^{4}}{4 x})

Cancel

\frac{12 x ^{4}}{4 x} : 3 x^{3}

= lo g_{10} (3 x^{3})

f (x) = 2 ln (x) + \frac{1}{2} ln (x + 4)

ln (7 \cdot e^{x})

f (x) = 4 [ln (x) - ln (x + 3) - ln (x - 3)]

f (x) = lo g_{3} (2 x) - lo g_{3} (x)

f (x) = lo g_{x} (2 \cdot 7)

What is log_{10}(12x^4)-log_{10}(4x) ?
The solution to log_{10}(12x^4)-log_{10}(4x) is log_{10}(3x^3)