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

The solution to expand log_{10}((2a^2)/b) is log_{10}(2)+2log_{10}(a)-log_{10}(b)

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (2 a^{2}) = lo g_{10} (2) + lo g_{10} (a^{2})

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

Apply log rule:

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

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

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

lo g_{b} (\frac{3.839}{0.32})

lo g_{3} (\frac{z}{9})

lo g_{10} (\frac{x ^{9} y ^{5}}{z ^{3}})

ln (x - 1) - ln (x + 8)

lo g_{10} (x) - 4 lo g_{10} (y) + 7 lo g_{10} (z)

What is expand log_{10}((2a^2)/b) ?
The solution to expand log_{10}((2a^2)/b) is log_{10}(2)+2log_{10}(a)-log_{10}(b)