en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

3 ln (2) = ln (2^{3})

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

Apply log rule:

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

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

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

Simplify

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

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

Popular Examples

simplify 1/3 [log_{6}(x)+log_{6}(7)]-[log_{6}(y)]simplify

\frac{1}{3} [lo g_{6} (x) + lo g_{6} (7)] - [lo g_{6} (y)]

simplify log_{10}(100x)simplify

lo g_{10} (100 x)

simplify ln(5)-2ln(4)simplify

ln (5) - 2 ln (4)

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

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

simplify-log_{10}(2\times 10^{-3})simplify

- lo g_{10} (2 \times 1 0^{- 3})

Frequently Asked Questions (FAQ)

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