What is expand log_{10}((2(7+x)^4)/(x^5)) ?

The solution to expand log_{10}((2(7+x)^4)/(x^5)) is log_{10}(2)+4log_{10}(7+x)-5log_{10}(x)

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expand log_{10}((2(7+x)^4)/(x^5))

expand

lo g_{10} (\frac{2 ( 7 + x ) ^{4}}{x ^{5}})

lo g_{10} (2) + 4 lo g_{10} (7 + x) - 5 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{2 ( 7 + x ) ^{4}}{x ^{5}})

Apply log rule:

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

lo g_{10} (\frac{2 ( 7 + x ) ^{4}}{x ^{5}}) = lo g_{10} (2 (7 + x)^{4}) - lo g_{10} (x^{5})

= lo g_{10} (2 (x + 7)^{4}) - lo g_{10} (x^{5})

Apply log rule:

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

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

= lo g_{10} (2 (7 + x)^{4}) - 5 lo g_{10} (x)

Apply log rule:

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

lo g_{10} (2 (7 + x)^{4}) = lo g_{10} (2) + lo g_{10} ((7 + x)^{4})

= lo g_{10} (2) + lo g_{10} ((x + 7)^{4}) - 5 lo g_{10} (x)

Apply log rule:

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

lo g_{10} ((7 + x)^{4}) = 4 lo g_{10} (7 + x)

= lo g_{10} (2) + 4 lo g_{10} (7 + x) - 5 lo g_{10} (x)

lo g_{g} (\frac{1}{g ^{3}})

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

lo g_{2} ((x - 4)^{3}) + lo g_{2} (x - 4) - 1

- lo g_{10} (2 \cdot 1 0^{(- 4)})

ln (\frac{d - R}{R})

What is expand log_{10}((2(7+x)^4)/(x^5)) ?
The solution to expand log_{10}((2(7+x)^4)/(x^5)) is log_{10}(2)+4log_{10}(7+x)-5log_{10}(x)