What is log_{2}(((x-2)^2(x+5))/5) ?

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

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simplify log_{2}(((x-2)^2(x+5))/5)

simplify

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

2 lo g_{2} (x - 2) + lo g_{2} (x + 5) - lo g_{2} (5)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

ln (315176)

5 lo g_{10} (x) - 3 lo g_{10} (y)

ln (\frac{e x}{3})

- ln \frac{( \frac{( 79 - 80 )}{( 10 - 80 )} )}{40}

f (x) = ln (x + 1) - ln (x + 2)

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