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

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

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

expand

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

lo g_{10} (3 a^{16}) - 2 lo g_{10} (b)

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= lo g_{10} (9 a^{16}) - lo g_{10} (b^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{10} (9 a^{16}) - 2 lo g_{10} (b)

9 a^{16} = 3 a^{16}

= lo g_{10} (3 a^{16}) - 2 lo g_{10} (b)

4 - lo g_{4} (16 y)

lo g_{10} (x^{2} + 2 x - 48) - lo g_{10} (x^{2} - 64)

- lo g_{10} (3.2 \cdot 1 0^{- 10})

lo g_{10} (\frac{x ^{2} y}{w ^{5} z})

- lo g_{2} (\frac{3}{8})

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