What is expand log_{7}(ab^4*c^3) ?

The solution to expand log_{7}(ab^4*c^3) is log_{7}(a)+4log_{7}(b)+3log_{7}(c)

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expand log_{7}(ab^4*c^3)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{7} (b^{4}) = 4 lo g_{7} (b)

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

Apply log rule:

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

lo g_{7} (c^{3}) = 3 lo g_{7} (c)

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

ln (x - 4) + ln (x - 1)

ln (x^{2} + x) - ln (x + 1)

19 lo g_{3} (x) - 82 lo g_{3} (y) + lo g_{3} (z)

lo g_{2} ((\frac{6 ^{4}}{11})^{5})

lo g_{10} (2 ab)

What is expand log_{7}(ab^4*c^3) ?
The solution to expand log_{7}(ab^4*c^3) is log_{7}(a)+4log_{7}(b)+3log_{7}(c)