What is ln(((1-4)(-2)^4)/1) ?

The solution to ln(((1-4)(-2)^4)/1) is 4ln(-2)+ln(-3)

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simplify ln(((1-4)(-2)^4)/1)

simplify

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

4 ln (- 2) + ln (- 3)

Solution steps

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

Apply log rule:

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

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

= ln ((- 2)^{4} (1 - 4)) - ln (1)

Apply log rule:

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

ln ((1 - 4) (- 2)^{4}) = ln (1 - 4) + ln ((- 2)^{4})

= ln (1 - 4) + ln ((- 2)^{4}) - ln (1)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((- 2)^{4}) = 4 ln (- 2)

= ln (1 - 4) + 4 ln (- 2) - ln (1)

Subtract the numbers:

1 - 4 = - 3

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

Apply log rule:

lo g_{a} (1) = 0

= ln (- 3) + 4 ln (- 2) - 0

ln (- 3) + 4 ln (- 2) - 0 = ln (- 3) + 4 ln (- 2)

= 4 ln (- 2) + ln (- 3)

ln (x (y - 1)^{2} e)

\frac{3 ln ( 2 )}{ln ( 6 )} - 8

ln (\frac{( 7 )}{( 7 - x )}) + 3

ln (x - 3) + ln (2)

- \frac{x ( ln ( x ) - ln ( y ) - 1 )}{y}

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