What is 2log_{10}(x+3)-5log_{10}(x-1) ?

The solution to 2log_{10}(x+3)-5log_{10}(x-1) is log_{10}(((x+3)^2)/((x-1)^5))

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simplify 2log_{10}(x+3)-5log_{10}(x-1)

simplify

2 lo g_{10} (x + 3) - 5 lo g_{10} (x - 1)

lo g_{10} (\frac{( x + 3 ) ^{2}}{( x - 1 ) ^{5}})

Solution steps

2 lo g_{10} (x + 3) - 5 lo g_{10} (x - 1)

Apply log rule:

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

2 lo g_{10} (x + 3) = lo g_{10} ((x + 3)^{2})

= lo g_{10} ((x + 3)^{2}) - 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 + 3)^{2}) - 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 + 3)^{2}) - lo g_{10} ((x - 1)^{5}) = lo g_{10} (\frac{( x + 3 ) ^{2}}{( x - 1 ) ^{5}})

= lo g_{10} (\frac{( x + 3 ) ^{2}}{( x - 1 ) ^{5}})

ln (5 e^{- i \frac{7 π}{4}})

ln (\frac{- 1}{( e ^{x} + c )})

\frac{27 ln ( 2 ) - 9 ln ( 3 )}{5}

ln (\frac{( 1 )}{12})

4 lo g_{8} (u) - 2 lo g_{8} (v)

What is 2log_{10}(x+3)-5log_{10}(x-1) ?
The solution to 2log_{10}(x+3)-5log_{10}(x-1) is log_{10}(((x+3)^2)/((x-1)^5))