What is ln(x)+ln(x)+3ln(sqrt(3)x) ?

The solution to ln(x)+ln(x)+3ln(sqrt(3)x) is ln(3sqrt(3)x^5)

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simplify ln(x)+ln(x)+3ln(sqrt(3)x)

simplify

ln (x) + ln (x) + 3 ln (3 x)

ln (33 x^{5})

Solution steps

ln (x) + ln (x) + 3 ln (3 x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Simplify

x (3 x)^{3} : 33 x^{4}

= ln (x) + ln (33 x^{4})

Apply log rule:

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

ln (x) + ln (33 x^{4}) = ln (33 x^{4} x)

= ln (33 x^{4} x)

Simplify

x \cdot 33 x^{4} : 33 x^{5}

= ln (33 x^{5})

lo g_{10} (\frac{2}{3})

ln (a - b) + ln (a + b)

ln v + v^{2} - ln ∣ v ∣

ln (\frac{15000}{15})

(x - 3) (ln (x - 3) - 2 ln (x^{2} - 9))

What is ln(x)+ln(x)+3ln(sqrt(3)x) ?
The solution to ln(x)+ln(x)+3ln(sqrt(3)x) is ln(3sqrt(3)x^5)