What is expand log_{2}((2(3x+4)^2)/(2^5(x+1)^2)) ?

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

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expand log_{2}((2(3x+4)^2)/(2^5(x+1)^2))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{2} (2^{5}) = 5 lo g_{2} (2)

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

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

5 lo g_{2} (2) = 5

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

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

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

Simplify

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

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

f (x) = ln (x) - \frac{1}{2} \cdot ln (x^{2} + 1)

ln (1.14 \cdot 86262850832)

ln (\frac{x ^{5} y ^{7}}{z w ^{4}})

ln (2) - ln (\frac{1}{3})

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