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Popular >

simplify 3ln(2)-1/2 ln(4)+ln(5)

Solution

simplify

3 ln (2) - \frac{1}{2} ln (4) + ln (5)

Solution

ln (20)

+1

Decimal Notation

2.99573 \dots

Solution steps

3 ln (2) - \frac{1}{2} ln (4) + ln (5)

Apply log rule:

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

\frac{1}{2} ln (4) = ln (4^{\frac{1}{2}})

= 3 ln (2) - ln (4^{\frac{1}{2}}) + ln (5)

Apply log rule:

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

ln (5) - ln (4^{\frac{1}{2}}) = ln (\frac{5}{4 ^{\frac{1}{2}}})

= 3 ln (2) + ln (\frac{5}{4 ^{\frac{1}{2}}})

4^{\frac{1}{2}} = 2

= 3 ln (2) + ln (\frac{5}{2})

Apply log rule:

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

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

= ln (2^{3}) + ln (\frac{5}{2})

Apply log rule:

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

ln (2^{3}) + ln (\frac{5}{2}) = ln (2^{3} \cdot \frac{5}{2})

= ln (2^{3} \cdot \frac{5}{2})

2^{3} \cdot \frac{5}{2} = 20

= ln (20)

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Frequently Asked Questions (FAQ)

What is 3ln(2)-1/2 ln(4)+ln(5) ?
The solution to 3ln(2)-1/2 ln(4)+ln(5) is ln(20)