What is expand log_{10}(\sqrt[4]{(b^7)/(b+6)}) ?

The solution to expand log_{10}(\sqrt[4]{(b^7)/(b+6)}) is 7/4 log_{10}(b)-1/4 log_{10}(b+6)

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expand log_{10}(\sqrt[4]{(b^7)/(b+6)})

expand

\frac{7}{4} lo g_{10} (b) - \frac{1}{4} lo g_{10} (b + 6)

Solution steps

Rewrite as

= lo g_{10} ((\frac{b ^{7}}{b + 6})^{\frac{1}{4}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{4} lo g_{10} (\frac{b ^{7}}{b + 6})

Simplify

lo g_{10} (\frac{b ^{7}}{b + 6}) : 7 lo g_{10} (b) - lo g_{10} (b + 6)

= \frac{1}{4} (7 lo g_{10} (b) - lo g_{10} (b + 6))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{4}, b = 7 lo g_{10} (b), c = lo g_{10} (b + 6)

= \frac{1}{4} \cdot 7 lo g_{10} (b) - \frac{1}{4} lo g_{10} (b + 6)

= 7 \cdot \frac{1}{4} lo g_{10} (b) - \frac{1}{4} lo g_{10} (b + 6)

7 \cdot \frac{1}{4} lo g_{10} (b) = \frac{7}{4} lo g_{10} (b)

= \frac{7}{4} lo g_{10} (b) - \frac{1}{4} lo g_{10} (b + 6)

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What is expand log_{10}(\sqrt[4]{(b^7)/(b+6)}) ?
The solution to expand log_{10}(\sqrt[4]{(b^7)/(b+6)}) is 7/4 log_{10}(b)-1/4 log_{10}(b+6)