What is 4log_{10}(3x^3)-12log_{10}(9x^8) ?

The solution to 4log_{10}(3x^3)-12log_{10}(9x^8) is -20log_{10}(3)-84log_{10}(x)

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simplify 4log_{10}(3x^3)-12log_{10}(9x^8)

simplify

4 lo g_{10} (3 x^{3}) - 12 lo g_{10} (9 x^{8})

- 20 lo g_{10} (3) - 84 lo g_{10} (x)

Solution steps

4 lo g_{10} (3 x^{3}) - 12 lo g_{10} (9 x^{8})

4 lo g_{10} (3 x^{3}) = lo g_{10} ((3 x^{3})^{4})

- 12 lo g_{10} (9 x^{8}) = - lo g_{10} ((9 x^{8})^{12})

= lo g_{10} ((3 x^{3})^{4}) - lo g_{10} ((9 x^{8})^{12})

Apply log rule:

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

lo g_{10} ((3 x^{3})^{4}) - lo g_{10} ((9 x^{8})^{12}) = lo g_{10} (\frac{( 3 x ^{3} ) ^{4}}{( 9 x ^{8} ) ^{12}})

= lo g_{10} (\frac{( 3 x ^{3} ) ^{4}}{( 9 x ^{8} ) ^{12}})

Cancel

\frac{( 3 x ^{3} ) ^{4}}{( 9 x ^{8} ) ^{12}} : \frac{1}{3 ^{20} x ^{84}}

= lo g_{10} (\frac{1}{3 ^{20} x ^{84}})

Simplify

\frac{1}{3 ^{20} x ^{84}} : (3^{20} x^{84})^{- 1}

= lo g_{10} ((3^{20} x^{84})^{- 1})

Apply log rule

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

lo g_{10} ((3^{20} x^{84})^{- 1}) = - 1 \cdot lo g_{10} (3^{20} x^{84})

= - 1 \cdot lo g_{10} (3^{20} x^{84})

Apply rule:

1 \cdot a = a

= - lo g_{10} (3^{20} x^{84})

Apply log rule:

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

lo g_{10} (3^{20} x^{84}) = lo g_{10} (3^{20}) + lo g_{10} (x^{84})

= - (lo g_{10} (3^{20}) + lo g_{10} (x^{84}))

lo g_{10} (3^{20}) = 20 lo g_{10} (3)

lo g_{10} (x^{84}) = 84 lo g_{10} (x)

= - (20 lo g_{10} (3) + 84 lo g_{10} (x))

Apply the distributive law:

- (a + b) = - a - b

- (20 lo g_{10} (3) + 84 lo g_{10} (x)) = - 20 lo g_{10} (3) - 84 lo g_{10} (x)

= - 20 lo g_{10} (3) - 84 lo g_{10} (x)

ln (9 x^{9}) + ln (10 x^{3})

ln (x + 2) + ln (3)

lo g_{10} (\frac{y ^{5}}{z ^{2} x})

\frac{ln ( ln ( \frac{1}{1 - 0.4} ) - 9 ln ( 250 ) )}{- 9}

ln (\frac{5}{4}) + ln (\frac{10}{3})

What is 4log_{10}(3x^3)-12log_{10}(9x^8) ?
The solution to 4log_{10}(3x^3)-12log_{10}(9x^8) is -20log_{10}(3)-84log_{10}(x)