What is ln(((x+4)^7)/(x^7sqrt(x+5))) ?

The solution to ln(((x+4)^7)/(x^7sqrt(x+5))) is 7ln(x+4)-7ln(x)-ln(sqrt(x+5))

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simplify ln(((x+4)^7)/(x^7sqrt(x+5)))

simplify

ln (\frac{( x + 4 ) ^{7}}{x ^{7} x + 5})

7 ln (x + 4) - 7 ln (x) - ln (x + 5)

Solution steps

ln (\frac{( x + 4 ) ^{7}}{x ^{7} x + 5})

Apply log rule:

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

ln (\frac{( x + 4 ) ^{7}}{x ^{7} x + 5}) = ln ((x + 4)^{7}) - ln (x^{7} x + 5)

= ln ((x + 4)^{7}) - ln (x^{7} x + 5)

Apply log rule:

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

ln ((x + 4)^{7}) = 7 ln (x + 4)

= 7 ln (x + 4) - ln (x^{7} x + 5)

Apply log rule:

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

ln (x^{7} x + 5) = ln (x^{7}) + ln (x + 5)

= 7 ln (x + 4) - (ln (x^{7}) + ln (x + 5))

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= 7 ln (x + 4) - (7 ln (x) + ln (x + 5))

- (7 ln (x) + ln (x + 5)) : - 7 ln (x) - ln (x + 5)

= 7 ln (x + 4) - 7 ln (x) - ln (x + 5)

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What is ln(((x+4)^7)/(x^7sqrt(x+5))) ?
The solution to ln(((x+4)^7)/(x^7sqrt(x+5))) is 7ln(x+4)-7ln(x)-ln(sqrt(x+5))