What is 3(ln(3)-ln(x^2))+(ln(x)-ln(9)) ?

The solution to 3(ln(3)-ln(x^2))+(ln(x)-ln(9)) is ln(3/(x^5))

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simplify 3(ln(3)-ln(x^2))+(ln(x)-ln(9))

simplify

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

ln (\frac{3}{x ^{5}})

Solution steps

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

= 3 ln (\frac{3}{x ^{2}}) + + ln (x) - ln (9)

Apply log rule:

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

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

= ln ((\frac{3}{x ^{2}})^{3}) + + ln (x) - ln (9)

Apply log rule:

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

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

= ln ((\frac{3}{x ^{2}})^{3} x) - ln (9)

Simplify

(\frac{3}{x ^{2}})^{3} x : \frac{27}{x ^{5}}

= ln (\frac{27}{x ^{5}}) - ln (9)

Apply log rule:

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

ln (\frac{27}{x ^{5}}) - ln (9) = ln (\frac{\frac{27}{x ^{5}}}{9})

= ln (\frac{\frac{27}{x ^{5}}}{9})

Simplify

\frac{\frac{27}{x ^{5}}}{9} : \frac{3}{x ^{5}}

= ln (\frac{3}{x ^{5}})

\frac{3}{16} [1 ln (1) + 4 ln (\frac{4}{3}) + 5 ln (\frac{5}{3}) + 2 ln (2)]

ln (\frac{1980 - 176}{894 - 176}) \cdot \frac{1}{3.058}

ln (x^{6} - x) - ln (x^{3} + 2)

\frac{ln ( 3 ) + ln ( h ) - ln ( 3 )}{h}

ln (x) + \frac{1}{2} ln (1 + u)

What is 3(ln(3)-ln(x^2))+(ln(x)-ln(9)) ?
The solution to 3(ln(3)-ln(x^2))+(ln(x)-ln(9)) is ln(3/(x^5))