What is expand log_{7}((u^3)/v) ?

The solution to expand log_{7}((u^3)/v) is 3log_{7}(u)-log_{7}(v)

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expand log_{7}((u^3)/v)

expand

lo g_{7} (\frac{u ^{3}}{v})

3 lo g_{7} (u) - lo g_{7} (v)

Solution steps

lo g_{7} (\frac{u ^{3}}{v})

Apply log rule:

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

lo g_{7} (\frac{u ^{3}}{v}) = lo g_{7} (u^{3}) - lo g_{7} (v)

= lo g_{7} (u^{3}) - lo g_{7} (v)

Apply log rule:

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

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

= 3 lo g_{7} (u) - lo g_{7} (v)

ln (6 x^{8})

\frac{1}{3} (2 ln (x) + ln (y) - 2 ln (z))

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

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

20 ln (\frac{1400}{1400 + 100 ( 10 )}) + 9.8 (10)

What is expand log_{7}((u^3)/v) ?
The solution to expand log_{7}((u^3)/v) is 3log_{7}(u)-log_{7}(v)