What is simplify-5ln(4x) ?

The solution to simplify-5ln(4x) is -10ln(2)-5ln(x)

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simplify-5ln(4x)

simplify

- 5 ln (4 x)

- 10 ln (2) - 5 ln (x)

Solution steps

- 5 ln (4 x)

Apply log rule:

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

5 ln (4 x) = 5 ln (4) + 5 ln (x)

= - (5 ln (x) + 5 ln (4))

5 ln (4) = 10 ln (2)

= - (5 ln (x) + 10 ln (2))

Distribute parentheses

= - (10 ln (2)) - (5 ln (x))

Apply minus-plus rules

+ (- a) = - a

= - 10 ln (2) - 5 ln (x)

- 3 ln ∣ x ∣ - ln ∣ x + 2 ∣ + 5 ln ∣ x - 2 ∣

lo g_{10} (\frac{1}{50})

ln (8) - ln (9)

ln \frac{( x ^{4} ( x + 1 ) ^{3} )}{( x - 1 ) ^{4}}

8 lo g_{b} (x) + 9 lo g_{b} (y) - 4 lo g_{b} (z)