What is expand log_{10}((a^2)/(b^{-3)c^4}) ?

The solution to expand log_{10}((a^2)/(b^{-3)c^4}) is 2log_{10}(a)+3log_{10}(b)-4log_{10}(c)

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expand log_{10}((a^2)/(b^{-3)c^4})

expand

lo g_{10} (\frac{a ^{2}}{b ^{- 3} c ^{4}})

2 lo g_{10} (a) + 3 lo g_{10} (b) - 4 lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{2}}{b ^{- 3} c ^{4}})

Apply log rule:

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

lo g_{10} (\frac{a ^{2}}{b ^{- 3} c ^{4}}) = lo g_{10} (a^{2}) - lo g_{10} (b^{- 3} c^{4})

= lo g_{10} (a^{2}) - lo g_{10} (b^{- 3} c^{4})

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^{- 3} c^{4})

Apply log rule:

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

lo g_{10} (b^{- 3} c^{4}) = lo g_{10} (b^{- 3}) + lo g_{10} (c^{4})

= 2 lo g_{10} (a) - (lo g_{10} (b^{- 3}) + lo g_{10} (c^{4}))

Apply log rule:

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

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

= 2 lo g_{10} (a) - (- 3 lo g_{10} (b) + lo g_{10} (c^{4}))

Apply log rule:

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

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

= 2 lo g_{10} (a) - (- 3 lo g_{10} (b) + 4 lo g_{10} (c))

- (- 3 lo g_{10} (b) + 4 lo g_{10} (c)) : 3 lo g_{10} (b) - 4 lo g_{10} (c)

= 2 lo g_{10} (a) + 3 lo g_{10} (b) - 4 lo g_{10} (c)

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 3 lo g_{b} (x)

lo g_{10} (x^{4}) y

lo g_{2} (6) + lo g_{2} (3)

lo g_{3} (\frac{c}{27})

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

What is expand log_{10}((a^2)/(b^{-3)c^4}) ?
The solution to expand log_{10}((a^2)/(b^{-3)c^4}) is 2log_{10}(a)+3log_{10}(b)-4log_{10}(c)