What is ln(1/x x^4) ?

The solution to ln(1/x x^4) is 3ln(x)

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simplify ln(1/x x^4)

simplify

ln (\frac{1}{x} x^{4})

3 ln (x)

Solution steps

ln (\frac{1}{x} x^{4})

Apply log rule:

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

ln (\frac{1}{x} x^{4}) = ln (\frac{1}{x}) + ln (x^{4})

= ln (\frac{1}{x}) + ln (x^{4})

Apply log rule:

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

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

= ln (\frac{1}{x}) + 4 ln (x)

Apply log rule:

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

ln (\frac{1}{x}) = ln (1) - ln (x)

= ln (1) - ln (x) + 4 ln (x)

Add similar elements:

- ln (x) + 4 ln (x) = 3 ln (x)

= ln (1) + 3 ln (x)

Apply log rule:

lo g_{a} (1) = 0

= 0 + 3 ln (x)

0 + 3 ln (x) = 3 ln (x)

= 3 ln (x)

- lo g_{10} (3.39880433 \times 1 0^{- 5})

lo g_{10} (\frac{7 z}{10})

ln (\frac{7 y}{5 z})

lo g_{4} (\frac{4}{x})

lo g_{a} (4 s^{2})