What is ln(1/((x^3sqrt(yz)))) ?

The solution to ln(1/((x^3sqrt(yz)))) is -(3ln(x)+ln(sqrt(yz)))

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simplify ln(1/((x^3sqrt(yz))))

simplify

ln (\frac{1}{( x ^{3} yz )})

- (3 ln (x) + ln (yz))

Solution steps

ln (\frac{1}{( x ^{3} yz )})

Apply log rule:

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

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

= ln (1) - ln (x^{3} yz)

Apply log rule:

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

ln (x^{3} yz) = ln (x^{3}) + ln (yz)

= ln (1) - (ln (x^{3}) + ln (yz))

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= ln (1) - (3 ln (x) + ln (yz))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (3 ln (x) + ln (yz))

0 - (3 ln (x) + ln (yz)) = - (3 ln (x) + ln (yz))

= - (3 ln (x) + ln (yz))

4 lo g_{3} (s) - 20 lo g_{3} (t)

- 2 ln (3) - 2 ln (2) + 2 ln (7)

ln (\frac{31.53}{31.53 - ( 0.01 \cdot 1400 )})

ln (x) + ln (x - 1) 2

- 3 ln (13) + 3 ln (18)

What is ln(1/((x^3sqrt(yz)))) ?
The solution to ln(1/((x^3sqrt(yz)))) is -(3ln(x)+ln(sqrt(yz)))