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Popular >

simplify 3ln(4)-ln(16)+ln(3)

Solution

simplify

3 ln (4) - ln (16) + ln (3)

Solution

ln (12)

+1

Decimal Notation

2.48490 \dots

Solution steps

3 ln (4) - ln (16) + ln (3)

Apply log rule:

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

ln (3) - ln (16) = ln (\frac{3}{16})

= 3 ln (4) + ln (\frac{3}{16})

Apply log rule:

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

3 ln (4) = ln (4^{3})

= ln (4^{3}) + ln (\frac{3}{16})

Apply log rule:

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

ln (4^{3}) + ln (\frac{3}{16}) = ln (4^{3} \cdot \frac{3}{16})

= ln (4^{3} \cdot \frac{3}{16})

4^{3} \cdot \frac{3}{16} = 12

= ln (12)

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Frequently Asked Questions (FAQ)

What is 3ln(4)-ln(16)+ln(3) ?
The solution to 3ln(4)-ln(16)+ln(3) is ln(12)