What is log_{2}(x-4)+5log_{2}(x+1)-3log_{2}(x-1) ?

The solution to log_{2}(x-4)+5log_{2}(x+1)-3log_{2}(x-1) is log_{2}(((x-4)(x+1)^5)/((x-1)^3))

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simplify log_{2}(x-4)+5log_{2}(x+1)-3log_{2}(x-1)

simplify

lo g_{2} (x - 4) + 5 lo g_{2} (x + 1) - 3 lo g_{2} (x - 1)

lo g_{2} (\frac{( x - 4 ) ( x + 1 ) ^{5}}{( x - 1 ) ^{3}})

Solution steps

lo g_{2} (x - 4) + 5 lo g_{2} (x + 1) - 3 lo g_{2} (x - 1)

Apply log rule:

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

5 lo g_{2} (x + 1) = lo g_{2} ((x + 1)^{5})

= lo g_{2} (x - 4) + lo g_{2} ((x + 1)^{5}) - 3 lo g_{2} (x - 1)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (x - 4) + lo g_{2} ((x + 1)^{5}) = lo g_{2} ((x + 1)^{5} (x - 4))

= lo g_{2} ((x - 4) (x + 1)^{5}) - 3 lo g_{2} (x - 1)

Apply log rule:

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

3 lo g_{2} (x - 1) = lo g_{2} ((x - 1)^{3})

= lo g_{2} ((x - 4) (x + 1)^{5}) - lo g_{2} ((x - 1)^{3})

Apply log rule:

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

lo g_{2} ((x - 4) (x + 1)^{5}) - lo g_{2} ((x - 1)^{3}) = lo g_{2} (\frac{( x + 1 ) ^{5} ( x - 4 )}{( x - 1 ) ^{3}})

= lo g_{2} (\frac{( x - 4 ) ( x + 1 ) ^{5}}{( x - 1 ) ^{3}})

ln (\frac{1}{64})

- ln (\frac{x ^{3}}{x ^{4} + c})

2 lo g_{2} (a) + 2 lo g_{2} (b) + 2 lo g_{2} (a + b)

4 lo g_{6} (a) - 7 lo g_{6} (b)

ln (y) - \frac{1}{2} (ln (1 + y) + ln (1 - y))

What is log_{2}(x-4)+5log_{2}(x+1)-3log_{2}(x-1) ?
The solution to log_{2}(x-4)+5log_{2}(x+1)-3log_{2}(x-1) is log_{2}(((x-4)(x+1)^5)/((x-1)^3))