What is ln((x(x^6+23))/(x^3+x-2)) ?

The solution to ln((x(x^6+23))/(x^3+x-2)) is ln(x)+ln(x^6+23)-ln(x^3+x-2)

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simplify ln((x(x^6+23))/(x^3+x-2))

simplify

ln (\frac{x ( x ^{6} + 23 )}{x ^{3} + x - 2})

ln (x) + ln (x^{6} + 23) - ln (x^{3} + x - 2)

Solution steps

ln (\frac{x ( x ^{6} + 23 )}{x ^{3} + x - 2})

Apply log rule:

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

ln (\frac{x ( x ^{6} + 23 )}{x ^{3} + x - 2}) = ln (x (x^{6} + 23)) - ln (x^{3} + x - 2)

= ln (x (x^{6} + 23)) - ln (x^{3} + x - 2)

Apply log rule:

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

ln (x (x^{6} + 23)) = ln (x) + ln (x^{6} + 23)

= ln (x) + ln (x^{6} + 23) - ln (x^{3} + x - 2)

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

lo g_{4} (\frac{y ^{8}}{16 x})

6 lo g_{5} (x) + 2 lo g_{5} (4 x) - \frac{1}{5} lo g_{5} (4 - x)

lo g_{x} (\frac{yz}{w})

- \frac{1}{3} ln (\frac{9}{19})

What is ln((x(x^6+23))/(x^3+x-2)) ?
The solution to ln((x(x^6+23))/(x^3+x-2)) is ln(x)+ln(x^6+23)-ln(x^3+x-2)