What is expand log_{10}((x/(y^4))^4) ?

The solution to expand log_{10}((x/(y^4))^4) is 4(log_{10}(x)-4log_{10}(y))

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expand log_{10}((x/(y^4))^4)

expand

lo g_{10} ((\frac{x}{y ^{4}})^{4})

4 (lo g_{10} (x) - 4 lo g_{10} (y))

Solution steps

lo g_{10} ((\frac{x}{y ^{4}})^{4})

Apply log rule:

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

lo g_{10} ((\frac{x}{y ^{4}})^{4}) = 4 lo g_{10} (\frac{x}{y ^{4}})

= 4 lo g_{10} (\frac{x}{y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{4}}) = lo g_{10} (x) - lo g_{10} (y^{4})

= 4 (lo g_{10} (x) - lo g_{10} (y^{4}))

Apply log rule:

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

lo g_{10} (y^{4}) = 4 lo g_{10} (y)

= 4 (lo g_{10} (x) - 4 lo g_{10} (y))

ln (6.85 \cdot 1 0^{43})

3 x + \frac{1}{2} (x - 1)^{2} + 5 ln ∣ x - 1 ∣ + \frac{1}{x - 1} - 2 ln ∣ x ∣ - 3

2 lo g_{10} (x) - 6 lo g_{10} (x - 9)

ln (x) - ln (6)

\frac{95}{100} \cdot ln (5 \cdot 1 0^{6}) + \frac{5}{100} \cdot ln (1000)

What is expand log_{10}((x/(y^4))^4) ?
The solution to expand log_{10}((x/(y^4))^4) is 4(log_{10}(x)-4log_{10}(y))