What is expand log_{10}((100x^2)/(27)) ?

The solution to expand log_{10}((100x^2)/(27)) is 2+2log_{10}(x)-3log_{10}(3)

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expand log_{10}((100x^2)/(27))

expand

lo g_{10} (\frac{100 x ^{2}}{27})

2 + 2 lo g_{10} (x) - 3 lo g_{10} (3)

Solution steps

lo g_{10} (\frac{100 x ^{2}}{27})

Apply log rule:

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

lo g_{10} (\frac{100 x ^{2}}{27}) = lo g_{10} (100 x^{2}) - lo g_{10} (27)

= lo g_{10} (100 x^{2}) - lo g_{10} (27)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (100 x^{2}) = lo g_{10} (100) + lo g_{10} (x^{2})

= lo g_{10} (100) + lo g_{10} (x^{2}) - lo g_{10} (27)

Apply log rule:

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

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

= lo g_{10} (100) + 2 lo g_{10} (x) - lo g_{10} (27)

lo g_{10} (100) = 2

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

= 2 + 2 lo g_{10} (x) - 3 lo g_{10} (3)

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

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}})

What is expand log_{10}((100x^2)/(27)) ?
The solution to expand log_{10}((100x^2)/(27)) is 2+2log_{10}(x)-3log_{10}(3)