How solve complicated logarithm?

Question

Can't someone please explain to me how to do question 6e and 10b? Thank!

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Answer 1 · 2017-10-03T05:53:12

Use definitions

6 e )
#log_3(x^2-3x-1) = 0#

Take #3^f# both sides. You get

#3^(log_3(x^2-3x-1)) = 3^0#

#x^2-3x-1 = 1#

Now solve the quadratic equation

#x^2-3x-2 = 0#

#x = (3\pm sqrt(9-4(-2)(1)))/2#

#x = (3\pm sqrt(17))/2#

#x = (3+4.1231)/2,(3-4.1231)/2#

#x = -0.5616,3.5616# (upto 5 significant figures)

10 b)
#log_10(5x)-log_10(3-2x)=1#

#log_10((5x)/(3-2x))=1#

Take antilog both sides

#(5x)/(3-2x) = 10#

#5x = 30 - 20x#

#25x = 30#

#x = 6/5#