What is expand log_{2}((b/c)^4) ?

The solution to expand log_{2}((b/c)^4) is 4(log_{2}(b)-log_{2}(c))

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expand log_{2}((b/c)^4)

expand

lo g_{2} ((\frac{b}{c})^{4})

4 (lo g_{2} (b) - lo g_{2} (c))

Solution steps

lo g_{2} ((\frac{b}{c})^{4})

Apply log rule:

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

lo g_{2} ((\frac{b}{c})^{4}) = 4 lo g_{2} (\frac{b}{c})

= 4 lo g_{2} (\frac{b}{c})

Apply log rule:

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

lo g_{2} (\frac{b}{c}) = lo g_{2} (b) - lo g_{2} (c)

= 4 (lo g_{2} (b) - lo g_{2} (c))

lo g_{t} (X \cdot Y)

ln (x^{4}) - ln (x^{16})

7 lo g_{2} (x) + 4 lo g_{2} (y) - 3 lo g_{2} (z)

\frac{3 \cdot ln ( 4 )}{8 ln ( 4 ) - 11 ln ( 3 )}

What is expand log_{2}((b/c)^4) ?
The solution to expand log_{2}((b/c)^4) is 4(log_{2}(b)-log_{2}(c))