What is 5log_{10}(x)-log^2_{10}(x) ?

The solution to 5log_{10}(x)-log^2_{10}(x) is log_{10}(x^4)

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simplify 5log_{10}(x)-log^2_{10}(x)

simplify

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

lo g_{10} (x^{4})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Cancel the common factor:

x

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

lo g_{2} (32767) - lo g_{2} (8.3)

ln (15) - ln (7)

ln (\frac{1000}{n})

ln (142) - 0.515 \cdot ln (100)

ln (\frac{68}{80})

What is 5log_{10}(x)-log^2_{10}(x) ?
The solution to 5log_{10}(x)-log^2_{10}(x) is log_{10}(x^4)