What is 5log_{10}(x)-4log_{10}(x+8) ?

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

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simplify 5log_{10}(x)-4log_{10}(x+8)

simplify

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

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

Solution steps

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

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 + 8)

Apply log rule:

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

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

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

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

ln (c^{1}) + 0.8 \cdot ln (c^{2})

14 - lo g_{10} (1.3 \cdot 1 0^{- 3})

ln (x ln (\frac{x}{e}))

- ln (10000) + 3 ln (5000 - 300)

ln (\frac{x ^{7}}{x ^{2} - 25})

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