What is log_{e}(x^4-16)-3log_{e}(x-2) ?

The solution to log_{e}(x^4-16)-3log_{e}(x-2) is ln(((x^2+4)(x+2))/((x-2)^2))

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simplify log_{e}(x^4-16)-3log_{e}(x-2)

simplify

lo g_{e} (x^{4} - 16) - 3 lo g_{e} (x - 2)

ln (\frac{( x ^{2} + 4 ) ( x + 2 )}{( x - 2 ) ^{2}})

Solution steps

lo g_{e} (x^{4} - 16) - 3 lo g_{e} (x - 2)

Apply log rule:

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

3 lo g_{e} (x - 2) = lo g_{e} ((x - 2)^{3})

= lo g_{e} (x^{4} - 16) - lo g_{e} ((x - 2)^{3})

Apply log rule:

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

lo g_{e} (x^{4} - 16) - lo g_{e} ((x - 2)^{3}) = lo g_{e} (\frac{x ^{4} - 16}{( x - 2 ) ^{3}})

= lo g_{e} (\frac{x ^{4} - 16}{( x - 2 ) ^{3}})

Simplify

\frac{x ^{4} - 16}{( x - 2 ) ^{3}} : \frac{( x ^{2} + 4 ) ( x + 2 )}{( x - 2 ) ^{2}}

= lo g_{e} (\frac{( x ^{2} + 4 ) ( x + 2 )}{( x - 2 ) ^{2}})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (\frac{( x ^{2} + 4 ) ( x + 2 )}{( x - 2 ) ^{2}})

ln (5 \cdot 1 0^{12 - 4})

59.7 ln (\frac{173}{285})

0.2149 + ln (- 1.045) + ln (1.5891) + ln (- 0.7544)

\frac{8 ( ln ∣ x + 3 ∣ - ln ∣ x + 4 ∣ )}{x}

What is log_{e}(x^4-16)-3log_{e}(x-2) ?
The solution to log_{e}(x^4-16)-3log_{e}(x-2) is ln(((x^2+4)(x+2))/((x-2)^2))