What is ln((2/x)^5*20) ?

The solution to ln((2/x)^5*20) is 5(ln(2)-ln(x))+ln(20)

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simplify ln((2/x)^5*20)

simplify

ln ((\frac{2}{x})^{5} \cdot 20)

5 (ln (2) - ln (x)) + ln (20)

Solution steps

ln ((\frac{2}{x})^{5} \cdot 20)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln ((\frac{2}{x})^{5} \cdot 20) = ln ((\frac{2}{x})^{5}) + ln (20)

= ln ((\frac{2}{x})^{5}) + ln (20)

Apply log rule:

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

ln ((\frac{2}{x})^{5}) = 5 ln (\frac{2}{x})

= 5 ln (\frac{2}{x}) + ln (20)

Apply log rule:

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

ln (\frac{2}{x}) = ln (2) - ln (x)

= 5 (- ln (x) + ln (2)) + ln (20)

ln (1 + x) - ln (x)

\frac{1}{2} ln (\frac{z}{2 x}) + \frac{1}{2} ln (\frac{z}{2 y})

\frac{1}{\frac{1}{25} ln ( \frac{2}{3} )} ln (\frac{16 - 20}{5 - 20})

\frac{5 π}{8} ln (5)

- 0.7 lo g_{10} (20.7) - 0.3 lo g_{10} (20.3)

What is ln((2/x)^5*20) ?
The solution to ln((2/x)^5*20) is 5(ln(2)-ln(x))+ln(20)