What is expand log_{3}((sqrt(x^7))/(y^5)) ?

The solution to expand log_{3}((sqrt(x^7))/(y^5)) is log_{3}(sqrt(x)sqrt(x^6))-5log_{3}(y)

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expand log_{3}((sqrt(x^7))/(y^5))

expand

lo g_{3} (\frac{x ^{7}}{y ^{5}})

lo g_{3} (x x^{6}) - 5 lo g_{3} (y)

Solution steps

lo g_{3} (\frac{x ^{7}}{y ^{5}})

Apply log rule:

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

lo g_{3} (\frac{x ^{7}}{y ^{5}}) = lo g_{3} (x^{7}) - lo g_{3} (y^{5})

= lo g_{3} (x^{7}) - lo g_{3} (y^{5})

Apply log rule:

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

lo g_{3} (y^{5}) = 5 lo g_{3} (y)

= lo g_{3} (x^{7}) - 5 lo g_{3} (y)

x^{7} = x x^{6}

= lo g_{3} (x x^{6}) - 5 lo g_{3} (y)

ln (2.8 \cdot 1 0^{- 4}) + \frac{90}{8.314 \cdot ( 35 + 273.15 )}

7 π (ln (7) - ln (2))

6 lo g_{b} (x) + 5 lo g_{b} (z)

ln (\frac{3}{3 + 1})

ln (5) + ln (3) - 2 ln (2)

What is expand log_{3}((sqrt(x^7))/(y^5)) ?
The solution to expand log_{3}((sqrt(x^7))/(y^5)) is log_{3}(sqrt(x)sqrt(x^6))-5log_{3}(y)