What is ln((x^5*(1-x)^{45})/(A^5B^{45)}) ?

The solution to ln((x^5*(1-x)^{45})/(A^5B^{45)}) is 5ln(x)+45ln(1-x)-5ln(A)-45ln(B)

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simplify ln((x^5*(1-x)^{45})/(A^5B^{45)})

simplify

ln (\frac{x ^{5} \cdot ( 1 - x ) ^{45}}{A ^{5} B ^{45}})

5 ln (x) + 45 ln (1 - x) - 5 ln (A) - 45 ln (B)

Solution steps

ln (\frac{x ^{5} ( 1 - x ) ^{45}}{A ^{5} B ^{45}})

Apply log rule:

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

ln (\frac{x ^{5} ( 1 - x ) ^{45}}{A ^{5} B ^{45}}) = ln (x^{5} (1 - x)^{45}) - ln (A^{5} B^{45})

= ln (x^{5} (- x + 1)^{45}) - ln (A^{5} B^{45})

Apply log rule:

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

ln (x^{5} (1 - x)^{45}) = ln (x^{5}) + ln ((1 - x)^{45}), ln (A^{5} B^{45}) = ln (A^{5}) + ln (B^{45})

= ln (x^{5}) + ln ((- x + 1)^{45}) - (ln (A^{5}) + ln (B^{45}))

Apply log rule:

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

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

= 5 ln (x) + ln ((1 - x)^{45}) - (ln (A^{5}) + ln (B^{45}))

Apply log rule:

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

ln ((1 - x)^{45}) = 45 ln (1 - x)

= 5 ln (x) + 45 ln (1 - x) - (ln (A^{5}) + ln (B^{45}))

Apply log rule:

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

ln (A^{5}) = 5 ln (A)

= 5 ln (x) + 45 ln (1 - x) - (5 ln (A) + ln (B^{45}))

Apply log rule:

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

ln (B^{45}) = 45 ln (B)

= 5 ln (x) + 45 ln (1 - x) - (5 ln (A) + 45 ln (B))

- (5 ln (A) + 45 ln (B)) : - 5 ln (A) - 45 ln (B)

= 5 ln (x) + 45 ln (1 - x) - 5 ln (A) - 45 ln (B)

0.22 5^{2} ln (8 \cdot 0.225)

lo g_{2} (\frac{75}{32})

10 lo g_{10} (\frac{1}{1 _{0}})

\frac{3 ln ( 5 )}{ln ( 5 ) - 2 ln ( 3 )}

lo g_{10} (\frac{x ^{2}}{y}) - 1

What is ln((x^5*(1-x)^{45})/(A^5B^{45)}) ?
The solution to ln((x^5*(1-x)^{45})/(A^5B^{45)}) is 5ln(x)+45ln(1-x)-5ln(A)-45ln(B)