What is 1/3 log_{10}(x)-log_{10}(5) ?

The solution to 1/3 log_{10}(x)-log_{10}(5) is log_{10}((x^{1/3})/5)

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simplify 1/3 log_{10}(x)-log_{10}(5)

simplify

\frac{1}{3} lo g_{10} (x) - lo g_{10} (5)

lo g_{10} (\frac{x ^{\frac{1}{3}}}{5})

Solution steps

\frac{1}{3} lo g_{10} (x) - lo g_{10} (5)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{3} lo g_{10} (x) = lo g_{10} (x^{\frac{1}{3}})

= lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (5)

Apply log rule:

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

lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (5) = lo g_{10} (\frac{x ^{\frac{1}{3}}}{5})

= lo g_{10} (\frac{x ^{\frac{1}{3}}}{5})

3 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣

ln (a^{4} b^{7})

\frac{1}{2} lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

2 ln (5) + 2 ln (x) - ln (y)

ln (\frac{x ^{3} ln ( 2 x )}{e ^{x} sin ( x )})

What is 1/3 log_{10}(x)-log_{10}(5) ?
The solution to 1/3 log_{10}(x)-log_{10}(5) is log_{10}((x^{1/3})/5)