What is expand log_{10}(x/(y^8)) ?

The solution to expand log_{10}(x/(y^8)) is log_{10}(x)-8log_{10}(y)

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expand log_{10}(x/(y^8))

expand

lo g_{10} (\frac{x}{y ^{8}})

lo g_{10} (x) - 8 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{y ^{8}})

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{8}}) = lo g_{10} (x) - lo g_{10} (y^{8})

= lo g_{10} (x) - lo g_{10} (y^{8})

Apply log rule:

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

lo g_{10} (y^{8}) = 8 lo g_{10} (y)

= lo g_{10} (x) - 8 lo g_{10} (y)

- ln (y) + ln (y + 1)

- 12 ln (8) + 12 ln (4)

- \frac{3}{4} lo g_{2} (\frac{3}{4}) - \frac{1}{4} lo g_{10} (x)

(\frac{1}{0.143}) ln (\frac{5 \cdot 1 0 ^{9}}{34000})

\frac{300}{2 \cdot π \cdot 450} \cdot ln (\frac{4 + 2 \cdot 45 0 ^{2}}{25})

What is expand log_{10}(x/(y^8)) ?
The solution to expand log_{10}(x/(y^8)) is log_{10}(x)-8log_{10}(y)