What is expand log_{a}((b^3)/(c^4d^7)) ?

The solution to expand log_{a}((b^3)/(c^4d^7)) is 3log_{a}(b)-4log_{a}(c)-7log_{a}(d)

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expand log_{a}((b^3)/(c^4d^7))

expand

lo g_{a} (\frac{b ^{3}}{c ^{4} d ^{7}})

3 lo g_{a} (b) - 4 lo g_{a} (c) - 7 lo g_{a} (d)

Solution steps

lo g_{a} (\frac{b ^{3}}{c ^{4} d ^{7}})

Apply log rule:

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

lo g_{a} (\frac{b ^{3}}{c ^{4} d ^{7}}) = lo g_{a} (b^{3}) - lo g_{a} (c^{4} d^{7})

= lo g_{a} (b^{3}) - lo g_{a} (c^{4} d^{7})

Apply log rule:

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

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

= 3 lo g_{a} (b) - lo g_{a} (c^{4} d^{7})

Apply log rule:

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

lo g_{a} (c^{4} d^{7}) = lo g_{a} (c^{4}) + lo g_{a} (d^{7})

= 3 lo g_{a} (b) - (lo g_{a} (c^{4}) + lo g_{a} (d^{7}))

Apply log rule:

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

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

= 3 lo g_{a} (b) - (4 lo g_{a} (c) + lo g_{a} (d^{7}))

Apply log rule:

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

lo g_{a} (d^{7}) = 7 lo g_{a} (d)

= 3 lo g_{a} (b) - (4 lo g_{a} (c) + 7 lo g_{a} (d))

- (4 lo g_{a} (c) + 7 lo g_{a} (d)) : - 4 lo g_{a} (c) - 7 lo g_{a} (d)

= 3 lo g_{a} (b) - 4 lo g_{a} (c) - 7 lo g_{a} (d)

4 ln (x) - \frac{1}{6} ln (y)

lo g_{10} (32 x)

ln (\frac{1}{1.7})

25 lo g_{6} (x) + 5 lo g_{6} (y)

- ln (\frac{2}{5})

What is expand log_{a}((b^3)/(c^4d^7)) ?
The solution to expand log_{a}((b^3)/(c^4d^7)) is 3log_{a}(b)-4log_{a}(c)-7log_{a}(d)