What is ln((z^7)/(sqrt(xy))) ?

The solution to ln((z^7)/(sqrt(xy))) is 7ln(z)-ln(sqrt(xy))

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simplify ln((z^7)/(sqrt(xy)))

simplify

ln (\frac{z ^{7}}{x y})

7 ln (z) - ln (x y)

Solution steps

ln (\frac{z ^{7}}{x y})

Apply log rule:

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

ln (\frac{z ^{7}}{x y}) = ln (z^{7}) - ln (x y)

= ln (z^{7}) - ln (x y)

Apply log rule:

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

ln (z^{7}) = 7 ln (z)

= 7 ln (z) - ln (x y)

lo g_{10} (4) + lo g_{10} (x + 1) - 4 lo g_{10} (x - 1)

lo g_{3} (z^{5} x)

lo g_{3} (\frac{4 ( x - 5 ) ^{2}}{x ^{4} ( x - 1 ) ^{3}})

ln (n) - ln (n + 1)

What is ln((z^7)/(sqrt(xy))) ?
The solution to ln((z^7)/(sqrt(xy))) is 7ln(z)-ln(sqrt(xy))