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

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

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

simplify

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

3 lo g_{10} (3) + 8 lo g_{10} (x)

Solution steps

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})

Apply log rule:

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

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

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

lo g_{10} (27) = 3 lo g_{10} (3)

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

= 3 lo g_{10} (3) + 8 lo g_{10} (x)

2 lo g_{2} (5) + lo g_{2} (3) - lo g_{2} (15)

3 lo g_{2} (A) + 5 lo g_{2} (B) - 2 lo g_{2} (C)

ln (\frac{1}{θ} e^{- \frac{x}{θ}})

lo g_{10} (\frac{z ^{5} y ^{4}}{x ^{5}})

ln (x^{2} + 9 x + 18) - ln (x + 6)

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