What is expand log_{5}((x/(2y))^8) ?

The solution to expand log_{5}((x/(2y))^8) is 8(log_{5}(x)-log_{5}(2y))

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expand log_{5}((x/(2y))^8)

expand

lo g_{5} ((\frac{x}{2 y})^{8})

8 (lo g_{5} (x) - lo g_{5} (2 y))

Solution steps

lo g_{5} ((\frac{x}{2 y})^{8})

Apply log rule:

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

lo g_{5} ((\frac{x}{2 y})^{8}) = 8 lo g_{5} (\frac{x}{2 y})

= 8 lo g_{5} (\frac{x}{2 y})

Apply log rule:

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

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

= 8 (lo g_{5} (x) - lo g_{5} (2 y))

\frac{( ln ( 0.25 ) + ln ( 0.5 ) + ln ( 0.75 ) ) \cdot 2 \cdot 0.25}{2}

\frac{ln ( 5.999 ) - ln ( 6 )}{5.999 - 6}

ln (3.5 \cdot 1 0^{- 14})

2 - 0.009 lo g_{10} (\frac{1.3 9 ^{2}}{4.9 3 ^{3}})

lo g_{2} (\frac{4000000}{\frac{1}{65536 \cdot 4000000} \cdot 1})

What is expand log_{5}((x/(2y))^8) ?
The solution to expand log_{5}((x/(2y))^8) is 8(log_{5}(x)-log_{5}(2y))