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

The solution to ln(x)+ln(x^3)-ln(sqrt(x))+ln(e) is ln(x^{7/2})+1

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simplify ln(x)+ln(x^3)-ln(sqrt(x))+ln(e)

simplify

ln (x) + ln (x^{3}) - ln (x) + ln (e)

ln (x^{\frac{7}{2}}) + 1

Solution steps

ln (x) + ln (x^{3}) - ln (x) + ln (e)

Apply log rule:

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

ln (x) + ln (x^{3}) = ln (x^{3} x)

= ln (x^{3} x) - ln (x) + ln (e)

Simplify

x x^{3} : x^{4}

= ln (x^{4}) - ln (x) + ln (e)

Apply log rule:

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

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

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

Simplify

\frac{x ^{4}}{x} : x^{\frac{7}{2}}

= ln (x^{\frac{7}{2}}) + ln (e)

Apply log rule:

lo g_{a} (a) = 1

= ln (x^{\frac{7}{2}}) + 1

lo g_{10} (\frac{5}{100})

3 ln (1000) - 2 lo g_{4} (\frac{1}{64}) + 6 ln (e)

ln (8) - \frac{1}{2} ln (k) - 3 ln (t) - \frac{1}{3} ln (m)

- lo g_{10} (2.3 \cdot 1 0^{- 3})

ln ∣ x ∣ - ln ∣ y ∣

What is ln(x)+ln(x^3)-ln(sqrt(x))+ln(e) ?
The solution to ln(x)+ln(x^3)-ln(sqrt(x))+ln(e) is ln(x^{7/2})+1