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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

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 - 2 x)^{2})

Apply log rule:

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

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

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

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Frequently Asked Questions (FAQ)

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