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Popular >

simplify ln(2^x(2-x)^5)

Solution

simplify

ln (2^{x} (2 - x)^{5})

Solution

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

Solution steps

ln (2^{x} (2 - x)^{5})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((2 - x)^{5}) = 5 ln (2 - x)

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

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Frequently Asked Questions (FAQ)

What is ln(2^x(2-x)^5) ?
The solution to ln(2^x(2-x)^5) is xln(2)+5ln(2-x)