What is expand log_{10}((6(5+x)^4)/(x^2)) ?

The solution to expand log_{10}((6(5+x)^4)/(x^2)) is log_{10}(6)+4log_{10}(5+x)-2log_{10}(x)

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expand log_{10}((6(5+x)^4)/(x^2))

expand

lo g_{10} (\frac{6 ( 5 + x ) ^{4}}{x ^{2}})

lo g_{10} (6) + 4 lo g_{10} (5 + x) - 2 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{6 ( 5 + x ) ^{4}}{x ^{2}})

Apply log rule:

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

lo g_{10} (\frac{6 ( 5 + x ) ^{4}}{x ^{2}}) = lo g_{10} (6 (5 + x)^{4}) - lo g_{10} (x^{2})

= lo g_{10} (6 (x + 5)^{4}) - lo g_{10} (x^{2})

Apply log rule:

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

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

= lo g_{10} (6 (5 + x)^{4}) - 2 lo g_{10} (x)

Apply log rule:

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

lo g_{10} (6 (5 + x)^{4}) = lo g_{10} (6) + lo g_{10} ((5 + x)^{4})

= lo g_{10} (6) + lo g_{10} ((x + 5)^{4}) - 2 lo g_{10} (x)

Apply log rule:

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

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

= lo g_{10} (6) + 4 lo g_{10} (5 + x) - 2 lo g_{10} (x)

2 ln (3) + ln (2)

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

\frac{ln ( 6 ) - ln ( 5 )}{4}

ln (\frac{7 x 1 + 6 x}{( x - 4 ) ^{4}})

lo g_{3} ((u^{4} v)^{6})

What is expand log_{10}((6(5+x)^4)/(x^2)) ?
The solution to expand log_{10}((6(5+x)^4)/(x^2)) is log_{10}(6)+4log_{10}(5+x)-2log_{10}(x)