What is 77ln(x)+23ln(1-x)+56.23 ?

The solution to 77ln(x)+23ln(1-x)+56.23 is ln(x^{77}(1-x)^{23})+56.23

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simplify 77ln(x)+23ln(1-x)+56.23

simplify

77 ln (x) + 23 ln (1 - x) + 56.23

ln (x^{77} (1 - x)^{23}) + 56.23

Solution steps

77 ln (x) + 23 ln (1 - x) + 56.23

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

77 ln (x) = ln (x^{77})

= ln (x^{77}) + 23 ln (- x + 1) + 56.23

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

23 ln (- x + 1) = ln ((- x + 1)^{23})

= ln (x^{77}) + ln ((- x + 1)^{23}) + 56.23

Apply log rule:

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

ln (x^{77}) + ln ((1 - x)^{23}) = ln (x^{77} (- x + 1)^{23})

= ln (x^{77} (1 - x)^{23}) + 56.23

lo g_{3} (\frac{81}{x ^{2} + 5})

lo g_{7} (11) + lo g_{7} (3)

lo g_{10} (\frac{z ^{6}}{x})

ln (\frac{x ^{2} 4 x + 1}{( x ^{3} + 5 ) ^{3}})

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

What is 77ln(x)+23ln(1-x)+56.23 ?
The solution to 77ln(x)+23ln(1-x)+56.23 is ln(x^{77}(1-x)^{23})+56.23