What is ln((nrt}{(\frac{3p)/(nrt))/p}) ?

The solution to ln((nrt}{(\frac{3p)/(nrt))/p}) is ln(n)+ln(r)+ln(t)-ln((3p)/(nrt))+ln(p)

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simplify ln((nrt}{(\frac{3p)/(nrt))/p})

simplify

ln \frac{n r t}{\frac{\frac{3 p}{n r t}}{p}}

ln (n) + ln (r) + ln (t) - ln (\frac{3 p}{n r t}) + ln (p)

Solution steps

ln \frac{n r t}{\frac{\frac{3 p}{n r t}}{p}}

Apply log rule:

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

ln \frac{n r t}{\frac{\frac{3 p}{n r t}}{p}} = ln (n r t) - ln (\frac{\frac{3 p}{n r t}}{p})

= ln (n r t) - ln (\frac{\frac{3 p}{n r t}}{p})

Apply log rule:

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

ln (\frac{\frac{3 p}{n r t}}{p}) = ln (\frac{3 p}{n r t}) - ln (p)

= ln (n r t) - (ln (\frac{3 p}{n r t}) - ln (p))

Apply log rule:

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

ln (n r t) = ln (n) + ln (r) + ln (t)

= ln (n) + ln (r) + ln (t) - (ln (\frac{3 p}{n r t}) - ln (p))

- (ln (\frac{3 p}{n r t}) - ln (p)) : - ln (\frac{3 p}{n r t}) + ln (p)

= ln (n) + ln (r) + ln (t) - ln (\frac{3 p}{n r t}) + ln (p)

2 ln (a) + 2 ln (b) - ln (a)

88 + 10 \cdot lo g_{10} (\frac{2}{4 \cdot 3.14 \cdot 1 0 ^{2}})

ln (b) + ln (a)

\frac{1}{7} (ln (x) + 6 ln (y))

What is ln((nrt}{(\frac{3p)/(nrt))/p}) ?
The solution to ln((nrt}{(\frac{3p)/(nrt))/p}) is ln(n)+ln(r)+ln(t)-ln((3p)/(nrt))+ln(p)