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Popular >

simplify ln(x^4(1-x)^{14})

Solution

simplify

ln (x^{4} (1 - x)^{14})

Solution

4 ln (x) + 14 ln (1 - x)

Solution steps

ln (x^{4} (1 - x)^{14})

Apply log rule:

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

ln (x^{4} (1 - x)^{14}) = ln (x^{4}) + ln ((1 - x)^{14})

= ln (x^{4}) + ln ((- x + 1)^{14})

Apply log rule:

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

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

= 4 ln (x) + ln ((1 - x)^{14})

Apply log rule:

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

ln ((1 - x)^{14}) = 14 ln (1 - x)

= 4 ln (x) + 14 ln (1 - x)

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Frequently Asked Questions (FAQ)

What is ln(x^4(1-x)^{14}) ?
The solution to ln(x^4(1-x)^{14}) is 4ln(x)+14ln(1-x)