What is 4x+5ln(x)-ln(2xy) ?

The solution to 4x+5ln(x)-ln(2xy) is 4x+ln((x^4)/(2y))

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simplify 4x+5ln(x)-ln(2xy)

simplify

4 x + 5 ln (x) - ln (2 x y)

4 x + ln (\frac{x ^{4}}{2 y})

Solution steps

4 x + 5 ln (x) - ln (2 x y)

Apply log rule:

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

5 ln (x) = ln (x^{5})

= 4 x + ln (x^{5}) - ln (2 x y)

Apply log rule:

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

ln (x^{5}) - ln (2 x y) = ln (\frac{x ^{5}}{2 x y})

= 4 x + ln (\frac{x ^{5}}{2 x y})

Cancel the common factor:

x

= 4 x + ln (\frac{x ^{4}}{2 y})

ln (u) + 3 ln (z + 1) - 2 ln (z + 2)

(2 ln (3) - ln (4)) - (2 ln (1) - ln (2))

10 \cdot lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 \cdot 1 0 ^{- 12}})

100 + 20 \cdot ln (\frac{65}{65 - 23})

ln (\frac{4}{9}) \cdot \frac{20}{ln ( \frac{4}{11} )}

What is 4x+5ln(x)-ln(2xy) ?
The solution to 4x+5ln(x)-ln(2xy) is 4x+ln((x^4)/(2y))