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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

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

Apply log rule:

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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