Solve the equation for x. ?

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1 Answer
Dec 14, 2017

#"a)" x=9.807#
#"b)" x=(1+sqrt(1+4e))/2#

Explanation:

#"(a) Take the logarithm of both sides :"#
#(x-7) ln(2) = ln(7)#
#=> x-7 = ln(7)/ln(2)#
#=> x = 7 + ln(7)/ln(2)#
#=> x = 9.807#
#"(b) Use ln(a)+ln(b) = ln(a*b), so we have"#
#ln(x(x-1)) = 1#
#"Take the exponential of both sides"#
#x(x-1) = e^1 = e#
#=> x²-x-e = 0#
#"this is a quadratic equation with discriminant"#
#disc : 1 + 4e = 11.873#
#=> x = (1 pm sqrt(1+4e))/2#
#"we have to take the solution with + sign to be able to"#
#"take ln(x-1) :"#
#=> x = (1+sqrt(1+4e))/2#