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

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

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

expand

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- (2 lo g_{10} (b) + lo g_{10} (c)) : - 2 lo g_{10} (b) - lo g_{10} (c)

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

lo g_{2} (5 \cdot 1 0^{9} \cdot 365 \cdot 24 \cdot 60 \cdot 60 \cdot 1 0^{6})

10 lo g_{10} (\frac{4 π \cdot 0.4}{( 0.075 ) ^{2}})

(5 (ln (5) - ln (2)))^{2} + (ln (5) - ln (2))^{2}

\frac{1}{2} ln (e^{2} + e) - \frac{1}{2} ln (1 + e)

ln (\frac{l}{2})

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