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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{x} (2 x)

ln (5 x^{2}) - ln (2 x^{2})

lo g_{10} (\frac{5}{2})

- \frac{66 ln ( \frac{11}{5} )}{ln ( 2 )}

lo g_{10} (5 x^{3} y)

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