What is 4log_{10}(x)-5log_{10}(x-1) ?

The solution to 4log_{10}(x)-5log_{10}(x-1) is log_{10}((x^4)/((x-1)^5))

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simplify 4log_{10}(x)-5log_{10}(x-1)

simplify

4 lo g_{10} (x) - 5 lo g_{10} (x - 1)

lo g_{10} (\frac{x ^{4}}{( x - 1 ) ^{5}})

Solution steps

4 lo g_{10} (x) - 5 lo g_{10} (x - 1)

Apply log rule:

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

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

= lo g_{10} (x^{4}) - 5 lo g_{10} (x - 1)

Apply log rule:

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

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

= lo g_{10} (x^{4}) - lo g_{10} ((x - 1)^{5})

Apply log rule:

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

lo g_{10} (x^{4}) - lo g_{10} ((x - 1)^{5}) = lo g_{10} (\frac{x ^{4}}{( x - 1 ) ^{5}})

= lo g_{10} (\frac{x ^{4}}{( x - 1 ) ^{5}})

5 lo g_{m} (y - 2) - 2 lo g_{m} (y + 7)

2 lo g_{m} (x - 3) - 4 lo g_{m} (x + 4)

ln (\frac{( - 6 e ^{5 x} )}{5})

- ln (\frac{w}{t})

(ln (50) - ln (12)) \cdot 600

What is 4log_{10}(x)-5log_{10}(x-1) ?
The solution to 4log_{10}(x)-5log_{10}(x-1) is log_{10}((x^4)/((x-1)^5))