forget how to solve for x with final exam coming up

Question

1) solve for x

a)log₂√8

b)log_x125=3/2

c)log₂(x-4) - log₂(x+2)=4

d)log₂(x²-2x)⁷=21

Answer 1

1) solve for x
a)log₂√8 There's no x but we can evaluate; = log₂(2^3/2) = 3/2
b)log_x125=3/2  Put this log (exponent!) as exponent on base x;

   125 = x^(3/2); raise this to (2/3) power: (5³)^2/3 = x; x =5² = 25
c)log₂(x-4) - log₂(x+2)=4

 log₂[(x-4)/(x+2)] = 4;

 exponentiate on base 2 ⇒(x-4)/(x+2)=16;

 you can take it from here!
d)log₂(x²-2x)⁷=21; 7log₂[x(x-2)]=21;log₂[x(x-2)]=3;

exponentiate on base 2 to get x(x-2)=9; this gives a quadratic equation that you can solve (be sure to check each answer).