What is 5log_{10}(x)-4log_{10}(x+5) ?

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

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simplify 5log_{10}(x)-4log_{10}(x+5)

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

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

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

ln (\frac{0.3}{0.1})

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- lo g_{10} (12 \cdot 1 0^{- 12})

ln (\frac{6}{9})

ln (\frac{( 2 - x ) ^{'}}{( 2 - x )})

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