What is 3(ln(3)-ln(x))+(ln(x)-ln(9)) ?

The solution to 3(ln(3)-ln(x))+(ln(x)-ln(9)) is ln(3/(x^2))

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simplify 3(ln(3)-ln(x))+(ln(x)-ln(9))

simplify

3 (ln (3) - ln (x)) + (ln (x) - ln (9))

ln (\frac{3}{x ^{2}})

Solution steps

3 (ln (3) - ln (x)) + (ln (x) - ln (9))

Apply log rule:

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

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

= 3 ln (\frac{3}{x}) + + ln (x) - ln (9)

Apply log rule:

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

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

= ln ((\frac{3}{x})^{3}) + + ln (x) - ln (9)

Apply log rule:

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

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

= ln ((\frac{3}{x})^{3} x) - ln (9)

Simplify

(\frac{3}{x})^{3} x : \frac{27}{x ^{2}}

= ln (\frac{27}{x ^{2}}) - ln (9)

Apply log rule:

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

ln (\frac{27}{x ^{2}}) - ln (9) = ln (\frac{\frac{27}{x ^{2}}}{9})

= ln (\frac{\frac{27}{x ^{2}}}{9})

Simplify

\frac{\frac{27}{x ^{2}}}{9} : \frac{3}{x ^{2}}

= ln (\frac{3}{x ^{2}})

ln (2 - 5) - ln (e^{2} + e^{4} + 1)

lo g_{2} (\frac{x}{3 y ^{2}})

ln ∣ x ∣ - ln x^{2}

- 1423.586575 \cdot lo g_{10} (\frac{0.1}{1})

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

What is 3(ln(3)-ln(x))+(ln(x)-ln(9)) ?
The solution to 3(ln(3)-ln(x))+(ln(x)-ln(9)) is ln(3/(x^2))