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

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

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

simplify

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

3 lo g_{10} (3) + 4 lo g_{10} (x)

Solution steps

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})

Apply log rule:

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

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

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

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

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

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

3 (lo g_{6} (z) - 4 lo g_{6} (x))

\frac{2}{3} ln (3)

lo g_{2} ((n + 3)^{2}) - lo g_{2} (n + 3)

lo g_{10} (2^{2}) + lo g_{10} (5^{3})

2 (ln (10) + ln (m))

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