What is expand ln((x^2-25)/(x^4)) ?

The solution to expand ln((x^2-25)/(x^4)) is ln(x^2-25)-4ln(x)

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expand ln((x^2-25)/(x^4))

expand

ln (\frac{x ^{2} - 25}{x ^{4}})

ln (x^{2} - 25) - 4 ln (x)

Solution steps

ln (\frac{x ^{2} - 25}{x ^{4}})

Apply log rule:

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

ln (\frac{x ^{2} - 25}{x ^{4}}) = ln (x^{2} - 25) - ln (x^{4})

= ln (x^{2} - 25) - ln (x^{4})

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= ln (x^{2} - 25) - 4 ln (x)

\frac{1}{0.039} ln (\frac{42.5}{42.46769})

10 ln (\frac{24000}{14000})

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

ln (4 x^{2} - 5) - ln (x^{2})

ln (\frac{45}{75})

What is expand ln((x^2-25)/(x^4)) ?
The solution to expand ln((x^2-25)/(x^4)) is ln(x^2-25)-4ln(x)