Question 127692
Solve for x:
a) log base4 (x+2) + log base4 (x-4)=2
log base4 (x+2)(x-4) = 2
(x+2)(x-4) = 4^2
x^2-2x-24=0
Factor:
(x-6)(x+4)=0
Positive answer:
x = 6
---------
Checking:
log base4 (8) + log base4 (2) = 2
log base4 [8*2) = 2
4^2 = 16
====================

b) log base2 (x^2-2) - log base2 (1/2x+5 = 1 
log base2 [(x^2-2)/((1/2)x+5)] = 1
[(x^2-2)/((1/2)x+5)] = 2
x^2-2 = x+10
x^2-x-12 = 0
(x-4)(x+3) = 0
Positive answer:
x = 4
-----------
Checking:
log base2(14) - log base2 (7) = 1
log base2[14/7] = 1
14/7 = 2
2 = 2
=========
Cheers,
Stan H.