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Popular >

simplify ln(1/3 w)+4w

Solution

simplify

ln (\frac{1}{3} w) + 4 w

Solution

4 w + ln (w) - ln (3)

Solution steps

ln (\frac{1}{3} w) + 4 w

Apply log rule:

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

ln (\frac{1}{3} w) = ln (\frac{1}{3}) + ln (w)

= ln (\frac{1}{3}) + ln (w) + 4 w

Apply log rule:

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

ln (\frac{1}{3}) = ln (1) - ln (3)

= ln (1) - ln (3) + ln (w) + 4 w

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (3) + ln (w) + 4 w

0 - ln (3) + ln (w) + 4 w = - ln (3) + ln (w) + 4 w

= 4 w + ln (w) - ln (3)

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Frequently Asked Questions (FAQ)

What is ln(1/3 w)+4w ?
The solution to ln(1/3 w)+4w is 4w+ln(w)-ln(3)