What is log_{10}((sqrt(9a^{16)})/(b^2)) ?

The solution to log_{10}((sqrt(9a^{16)})/(b^2)) is log_{10}(3)+8log_{10}(a)-2log_{10}(b)

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simplify log_{10}((sqrt(9a^{16)})/(b^2))

simplify

lo g_{10} (\frac{9 a ^{16}}{b ^{2}})

lo g_{10} (3) + 8 lo g_{10} (a) - 2 lo g_{10} (b)

Solution steps

lo g_{10} (\frac{9 a ^{16}}{b ^{2}})

Simplify

9 a^{16} : 3 a^{8}

= lo g_{10} (\frac{3 a ^{8}}{b ^{2}})

Apply log rule:

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

lo g_{10} (\frac{3 a ^{8}}{b ^{2}}) = lo g_{10} (3 a^{8}) - lo g_{10} (b^{2})

= lo g_{10} (3 a^{8}) - lo g_{10} (b^{2})

lo g_{10} (3 a^{8}) = lo g_{10} (3) + 8 lo g_{10} (a)

lo g_{10} (b^{2}) = 2 lo g_{10} (b)

= lo g_{10} (3) + 8 lo g_{10} (a) - 2 lo g_{10} (b)

lo g_{10} (\frac{x}{1})

ln^{2} (2 x)

\frac{1}{5} - 5 ln (\frac{1}{5})

2 lo g_{10} (8) + 2 lo g_{10} (x)

What is log_{10}((sqrt(9a^{16)})/(b^2)) ?
The solution to log_{10}((sqrt(9a^{16)})/(b^2)) is log_{10}(3)+8log_{10}(a)-2log_{10}(b)