What is ln(1/x)+ln(sqrt(x))-ln(x^3) ?

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

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simplify ln(1/x)+ln(sqrt(x))-ln(x^3)

simplify

ln (\frac{1}{x}) + ln (x) - ln (x^{3})

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

Solution steps

ln (\frac{1}{x}) + ln (x) - ln (x^{3})

Apply log rule:

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

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

= ln (\frac{1}{x} x) - ln (x^{3})

Simplify

\frac{1}{x} x : \frac{x}{x}

= ln (\frac{x}{x}) - ln (x^{3})

Apply log rule:

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

ln (\frac{x}{x}) - ln (x^{3}) = ln (\frac{\frac{x}{x}}{x ^{3}})

= ln (\frac{\frac{x}{x}}{x ^{3}})

Simplify

\frac{\frac{x}{x}}{x ^{3}} : \frac{x}{x ^{4}}

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

ln (\frac{140}{125})

\frac{1}{5} ln ∣ x + 1 ∣ + \frac{4}{5} ln ∣ x - 4 ∣

5 lo g_{b} (t) + 2 lo g_{b} (w)

ln (a e^{x}) + ln (b e^{- x})

ln (x d x)

What is ln(1/x)+ln(sqrt(x))-ln(x^3) ?
The solution to ln(1/x)+ln(sqrt(x))-ln(x^3) is ln((sqrt(x))/(x^4))