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

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

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

simplify

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

lo g_{10} (27 x^{8})

Solution steps

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

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

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

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

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

Cancel

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

= lo g_{10} (27 x^{8})

lo g_{10} (81) - lo g_{10} (\frac{64}{36})

5 ln (a) + \frac{ln ( b )}{3} - 3 ln (c)

ln (\frac{1}{72})

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{10} (\frac{x}{y})

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