What is log_{10}((4(8+x)^2)/(x^5)) ?

The solution to log_{10}((4(8+x)^2)/(x^5)) is 2log_{10}(2)+2log_{10}(8+x)-5log_{10}(x)

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simplify log_{10}((4(8+x)^2)/(x^5))

simplify

lo g_{10} (\frac{4 ( 8 + x ) ^{2}}{x ^{5}})

2 lo g_{10} (2) + 2 lo g_{10} (8 + x) - 5 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{4 ( 8 + x ) ^{2}}{x ^{5}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{4 ( 8 + x ) ^{2}}{x ^{5}}) = lo g_{10} (4 (8 + x)^{2}) - lo g_{10} (x^{5})

= lo g_{10} (4 (8 + x)^{2}) - lo g_{10} (x^{5})

lo g_{10} (4 (8 + x)^{2}) = 2 lo g_{10} (2) + 2 lo g_{10} (8 + x)

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

= 2 lo g_{10} (2) + 2 lo g_{10} (8 + x) - 5 lo g_{10} (x)

ln (5) + \frac{1}{3} ln (27)

ln (e (x - 2))

3 lo g_{2} (x) + lo g_{2} (5)

lo g_{6} (x - 3) + lo g_{6} (x)

lo g_{10} (\frac{x}{10 y ^{3}})

What is log_{10}((4(8+x)^2)/(x^5)) ?
The solution to log_{10}((4(8+x)^2)/(x^5)) is 2log_{10}(2)+2log_{10}(8+x)-5log_{10}(x)