What is expand log_{4}(sqrt((b^3)/(b+7))) ?

The solution to expand log_{4}(sqrt((b^3)/(b+7))) is 3/2 log_{4}(b)-1/2 log_{4}(b+7)

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expand log_{4}(sqrt((b^3)/(b+7)))

expand

lo g_{4} (\frac{b ^{3}}{b + 7})

\frac{3}{2} lo g_{4} (b) - \frac{1}{2} lo g_{4} (b + 7)

Solution steps

lo g_{4} (\frac{b ^{3}}{b + 7})

Rewrite as

= lo g_{4} ((\frac{b ^{3}}{b + 7})^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} lo g_{4} (\frac{b ^{3}}{b + 7})

Simplify

lo g_{4} (\frac{b ^{3}}{b + 7}) : 3 lo g_{4} (b) - lo g_{4} (b + 7)

= \frac{1}{2} (3 lo g_{4} (b) - lo g_{4} (b + 7))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{2}, b = 3 lo g_{4} (b), c = lo g_{4} (b + 7)

= \frac{1}{2} \cdot 3 lo g_{4} (b) - \frac{1}{2} lo g_{4} (b + 7)

= 3 \cdot \frac{1}{2} lo g_{4} (b) - \frac{1}{2} lo g_{4} (b + 7)

3 \cdot \frac{1}{2} lo g_{4} (b) = \frac{3}{2} lo g_{4} (b)

= \frac{3}{2} lo g_{4} (b) - \frac{1}{2} lo g_{4} (b + 7)

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What is expand log_{4}(sqrt((b^3)/(b+7))) ?
The solution to expand log_{4}(sqrt((b^3)/(b+7))) is 3/2 log_{4}(b)-1/2 log_{4}(b+7)