What is ln(e^{4x}((x^5-8x+6)/(cos(x)))) ?

The solution to ln(e^{4x}((x^5-8x+6)/(cos(x)))) is 4xln(e)++ln(x^5-8x+6)-ln(cos(x))

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simplify ln(e^{4x}((x^5-8x+6)/(cos(x))))

simplify

ln (e^{4 x} (\frac{x ^{5} - 8 x + 6}{cos ( x )}))

4 x ln (e) + + ln (x^{5} - 8 x + 6) - ln (cos (x))

Solution steps

ln (e^{4 x} (\frac{x ^{5} - 8 x + 6}{cos ( x )}))

Apply log rule:

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

ln (e^{4 x} (\frac{x ^{5} - 8 x + 6}{cos ( x )})) = ln (e^{4 x}) + ln (\frac{x ^{5} - 8 x + 6}{cos ( x )})

= ln (e^{4 x}) + ln (\frac{x ^{5} - 8 x + 6}{cos ( x )})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{4 x}) = 4 x ln (e)

= 4 x ln (e) + ln (\frac{x ^{5} - 8 x + 6}{cos ( x )})

Apply log rule:

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

ln (\frac{x ^{5} - 8 x + 6}{cos ( x )}) = ln (x^{5} - 8 x + 6) - ln (cos (x))

= 4 ln (e) x + + ln (x^{5} - 8 x + 6) - ln (cos (x))

\frac{1}{4} [3 ln (x + 7) - ln (x) - ln (x^{2} - 25)]

2 ln (x + 2) - ln (x)

lo g_{3} (9 s)

lo g_{10} (587) - lo g_{10} (266)

What is ln(e^{4x}((x^5-8x+6)/(cos(x)))) ?
The solution to ln(e^{4x}((x^5-8x+6)/(cos(x)))) is 4xln(e)++ln(x^5-8x+6)-ln(cos(x))