What is 4log_{10}(3x^2)-1/2 log_{10}(9x^8) ?

The solution to 4log_{10}(3x^2)-1/2 log_{10}(9x^8) is log_{10}(27x^4)

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simplify 4log_{10}(3x^2)-1/2 log_{10}(9x^8)

simplify

4 lo g_{10} (3 x^{2}) - \frac{1}{2} lo g_{10} (9 x^{8})

lo g_{10} (27 x^{4})

Solution steps

4 lo g_{10} (3 x^{2}) - \frac{1}{2} lo g_{10} (9 x^{8})

4 lo g_{10} (3 x^{2}) = lo g_{10} ((3 x^{2})^{4})

- \frac{1}{2} lo g_{10} (9 x^{8}) = - lo g_{10} ((9 x^{8})^{\frac{1}{2}})

= lo g_{10} ((3 x^{2})^{4}) - lo g_{10} ((9 x^{8})^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} ((3 x^{2})^{4}) - lo g_{10} ((9 x^{8})^{\frac{1}{2}}) = lo g_{10} (\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}})

= lo g_{10} (\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}})

Cancel

\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}} : 27 x^{4}

= lo g_{10} (27 x^{4})

lo g_{10} (a x^{b})

ln ∣ 3 - 2 ∣ - \frac{3}{2} ln ∣ 2 \cdot 3 - 1 ∣ + 2 ln ∣ 3 + 3 ∣

lo g_{2} (\frac{a ^{2} - 9}{8})

- lo g_{10} (6.5 \cdot 1 0^{- 3})

ln (\frac{9}{7 x ^{7} y})

What is 4log_{10}(3x^2)-1/2 log_{10}(9x^8) ?
The solution to 4log_{10}(3x^2)-1/2 log_{10}(9x^8) is log_{10}(27x^4)