What is ln((P_{2})/(P^1))+ln((V_{2})/(V_{1)})k ?

The solution to ln((P_{2})/(P^1))+ln((V_{2})/(V_{1)})k is ln(P_{2})-ln(P)+kln((V_{2})/(V_{1)})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((P_{2})/(P^1))+ln((V_{2})/(V_{1)})k

simplify

ln (\frac{P _{2}}{P ^{1}}) + ln (\frac{V _{2}}{V _{1}}) k

ln (P_{2}) - ln (P) + k ln (\frac{V _{2}}{V _{1}})

Solution steps

ln (\frac{P _{2}}{P ^{1}}) + ln (\frac{V _{2}}{V _{1}}) k

Apply log rule:

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

ln (\frac{P _{2}}{P ^{1}}) = ln (P_{2}) - ln (P^{1})

= ln (P_{2}) - ln (P^{1}) + k ln (\frac{V _{2}}{V _{1}})

Apply log rule:

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

ln (P^{1}) = 1 \cdot ln (P)

= ln (P_{2}) - 1 \cdot ln (P) + ln (\frac{V _{2}}{V _{1}}) k

Multiply:

1 \cdot ln (P) = ln (P)

= ln (P_{2}) - ln (P) + k ln (\frac{V _{2}}{V _{1}})

\frac{1}{0.00003} ln (\frac{75 - 15}{25 - 15})

ln (14) + ln (3)

6 ln (2) - 4 ln (y)

\frac{1}{2} ln (11) - \frac{1}{2} ln (3)

ln (\frac{107}{100})

What is ln((P_{2})/(P^1))+ln((V_{2})/(V_{1)})k ?
The solution to ln((P_{2})/(P^1))+ln((V_{2})/(V_{1)})k is ln(P_{2})-ln(P)+kln((V_{2})/(V_{1)})