What is ln(x^3)-ln(x^6)+ln(x^4) ?

The solution to ln(x^3)-ln(x^6)+ln(x^4) is ln(x)

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simplify ln(x^3)-ln(x^6)+ln(x^4)

simplify

ln (x^{3}) - ln (x^{6}) + ln (x^{4})

ln (x)

Solution steps

ln (x^{3}) - ln (x^{6}) + ln (x^{4})

Apply log rule:

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

ln (x^{3}) - ln (x^{6}) = ln (\frac{x ^{3}}{x ^{6}})

= ln (\frac{x ^{3}}{x ^{6}}) + ln (x^{4})

Simplify

\frac{x ^{3}}{x ^{6}} : \frac{1}{x ^{3}}

= ln (\frac{1}{x ^{3}}) + ln (x^{4})

Apply log rule:

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

ln (\frac{1}{x ^{3}}) + ln (x^{4}) = ln (\frac{1}{x ^{3}} x^{4})

= ln (\frac{1}{x ^{3}} x^{4})

Simplify

\frac{1}{x ^{3}} x^{4} : x

= ln (x)

lo g_{10} (y z^{3})

\frac{ln ( 6 ) + ln ( 2 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

\frac{1}{3} lo g_{c} (x) + 4 lo g_{c} (y) - 5 lo g_{c} (x)

lo g_{3} (3 x)

ln (\frac{( e ^{x} )}{1 + e ^{x}})

What is ln(x^3)-ln(x^6)+ln(x^4) ?
The solution to ln(x^3)-ln(x^6)+ln(x^4) is ln(x)