What is expand log_{10}((a^2)/(b^4sqrt(c))) ?

The solution to expand log_{10}((a^2)/(b^4sqrt(c))) is 2log_{10}(a)-4log_{10}(b)-log_{10}(sqrt(c))

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expand log_{10}((a^2)/(b^4sqrt(c)))

expand

lo g_{10} (\frac{a ^{2}}{b ^{4} c})

2 lo g_{10} (a) - 4 lo g_{10} (b) - lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{2}}{b ^{4} c})

Apply log rule:

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

lo g_{10} (\frac{a ^{2}}{b ^{4} c}) = lo g_{10} (a^{2}) - lo g_{10} (b^{4} c)

= lo g_{10} (a^{2}) - lo g_{10} (b^{4} c)

Apply log rule:

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

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

= 2 lo g_{10} (a) - lo g_{10} (b^{4} c)

Apply log rule:

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

lo g_{10} (b^{4} c) = lo g_{10} (b^{4}) + lo g_{10} (c)

= 2 lo g_{10} (a) - (lo g_{10} (b^{4}) + lo g_{10} (c))

Apply log rule:

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

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

= 2 lo g_{10} (a) - (4 lo g_{10} (b) + lo g_{10} (c))

- (4 lo g_{10} (b) + lo g_{10} (c)) : - 4 lo g_{10} (b) - lo g_{10} (c)

= 2 lo g_{10} (a) - 4 lo g_{10} (b) - lo g_{10} (c)

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\frac{1}{2} \cdot lo g_{2} (9 x^{16}) - \frac{2}{3} \cdot lo g_{2} (8 x^{3})

ln (\frac{1 + x}{1 - x})

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What is expand log_{10}((a^2)/(b^4sqrt(c))) ?
The solution to expand log_{10}((a^2)/(b^4sqrt(c))) is 2log_{10}(a)-4log_{10}(b)-log_{10}(sqrt(c))