What is expand ln((4p^3)/(5q^4)) ?

The solution to expand ln((4p^3)/(5q^4)) is 2ln(2)+3ln(p)-ln(5)-4ln(q)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ln((4p^3)/(5q^4))

expand

ln (\frac{4 p ^{3}}{5 q ^{4}})

2 ln (2) + 3 ln (p) - ln (5) - 4 ln (q)

Solution steps

ln (\frac{4 p ^{3}}{5 q ^{4}})

Apply log rule:

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

ln (\frac{4 p ^{3}}{5 q ^{4}}) = ln (4 p^{3}) - ln (5 q^{4})

= ln (4 p^{3}) - ln (5 q^{4})

Apply log rule:

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

ln (4 p^{3}) = ln (4) + ln (p^{3}), ln (5 q^{4}) = ln (5) + ln (q^{4})

= ln (4) + ln (p^{3}) - (ln (q^{4}) + ln (5))

Apply log rule:

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

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

= ln (4) + 3 ln (p) - (ln (5) + ln (q^{4}))

Apply log rule:

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

ln (q^{4}) = 4 ln (q)

= ln (4) + 3 ln (p) - (ln (5) + 4 ln (q))

ln (4) = 2 ln (2)

= 2 ln (2) + 3 ln (p) - (4 ln (q) + ln (5))

- (ln (5) + 4 ln (q)) : - ln (5) - 4 ln (q)

= 2 ln (2) + 3 ln (p) - ln (5) - 4 ln (q)

ln (\frac{1.6}{12})

- \frac{2 ln ( 2 )}{ln ( 5 ) - 2 ln ( 2 )}

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

ln (\frac{4}{x}) + ln (\frac{2}{x ^{3}})

lo g_{a} (\frac{( x - 5 ) ^{6}}{( x + 7 ) ^{7}})

What is expand ln((4p^3)/(5q^4)) ?
The solution to expand ln((4p^3)/(5q^4)) is 2ln(2)+3ln(p)-ln(5)-4ln(q)