What is 2ln(a)-ln(3b)+2ln(2) ?

The solution to 2ln(a)-ln(3b)+2ln(2) is ln((4a^2)/(3b))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(a)-ln(3b)+2ln(2)

simplify

2 ln (a) - ln (3 b) + 2 ln (2)

ln (\frac{4 a ^{2}}{3 b})

Solution steps

2 ln (a) - ln (3 b) + 2 ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (a) = ln (a^{2})

= ln (a^{2}) - ln (3 b) + 2 ln (2)

Apply log rule:

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

ln (a^{2}) - ln (3 b) = ln (\frac{a ^{2}}{3 b})

= ln (\frac{a ^{2}}{3 b}) + 2 ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (2) = ln (2^{2})

= ln (\frac{a ^{2}}{3 b}) + ln (2^{2})

Apply log rule:

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

ln (\frac{a ^{2}}{3 b}) + ln (2^{2}) = ln (2^{2} \cdot \frac{a ^{2}}{3 b})

= ln (2^{2} \cdot \frac{a ^{2}}{3 b})

Simplify

\frac{a ^{2}}{3 b} \cdot 2^{2} : \frac{4 a ^{2}}{3 b}

= ln (\frac{4 a ^{2}}{3 b})

lo g_{10} (3 x) - 1

lo g_{b} (19 x^{5} y)

lo g_{10} (\frac{y ^{6}}{z})

What is 2ln(a)-ln(3b)+2ln(2) ?
The solution to 2ln(a)-ln(3b)+2ln(2) is ln((4a^2)/(3b))