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

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

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expand log_{a}(((a^4)sqrt(b))/(c^3))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{a} (c^{3}) = 3 lo g_{a} (c)

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

Apply log rule:

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

lo g_{a} (a^{4} b) = lo g_{a} (a^{4}) + lo g_{a} (b)

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

Apply log rule:

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

lo g_{a} (a^{4}) = 4 lo g_{a} (a)

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

4 lo g_{a} (a) = 4

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

lo g_{10} (\frac{10}{1 + 4 e ^{- 0.8 x}})

ln (200 (\frac{12}{23})^{\frac{1}{3}})

ln (\frac{9 x ^{2} - 6 y ^{2} - 36}{36})

2 x + ln (\frac{x ^{6}}{( x ^{2} - 2 x - 1 )})

lo g_{a} (\frac{x - x ^{\frac{1}{2}}}{( x - y ) ^{3}})

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