What is expand log_{10}(((u^6)/v)^4) ?

The solution to expand log_{10}(((u^6)/v)^4) is 4(6log_{10}(u)-log_{10}(v))

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expand log_{10}(((u^6)/v)^4)

expand

lo g_{10} ((\frac{u ^{6}}{v})^{4})

4 (6 lo g_{10} (u) - lo g_{10} (v))

Solution steps

lo g_{10} ((\frac{u ^{6}}{v})^{4})

Apply log rule:

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

lo g_{10} ((\frac{u ^{6}}{v})^{4}) = 4 lo g_{10} (\frac{u ^{6}}{v})

= 4 lo g_{10} (\frac{u ^{6}}{v})

Apply log rule:

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

lo g_{10} (\frac{u ^{6}}{v}) = lo g_{10} (u^{6}) - lo g_{10} (v)

= 4 (lo g_{10} (u^{6}) - lo g_{10} (v))

Apply log rule:

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

lo g_{10} (u^{6}) = 6 lo g_{10} (u)

= 4 (6 lo g_{10} (u) - lo g_{10} (v))

ln (x - 4) [ln (x - 5) + ln (x + 5)]

ln (\frac{10}{12})

- ln (\frac{7163}{7})

c \cdot e^{40 \cdot (\frac{1}{20} \cdot l n (\frac{19}{20})) = 39}

3 lo g_{3^{^{'}}} (- 2 lo g_{6} (x))

What is expand log_{10}(((u^6)/v)^4) ?
The solution to expand log_{10}(((u^6)/v)^4) is 4(6log_{10}(u)-log_{10}(v))