SOLUTION: If x^a = y^b = k and x^c = y^d = t , then which of the following is true: A) ac=bd B) ad=bc C) a/d = c/b D) a^c = b^d E) a+c = b+d

Algebra ->  Expressions-with-variables -> SOLUTION: If x^a = y^b = k and x^c = y^d = t , then which of the following is true: A) ac=bd B) ad=bc C) a/d = c/b D) a^c = b^d E) a+c = b+d      Log On


   

Question 1168698: If x^a = y^b = k and x^c = y^d = t , then which of the following is true:
A) ac=bd
B) ad=bc
C) a/d = c/b
D) a^c = b^d
E) a+c = b+d
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
x%5Ea++=+k+ → log%28+x%29++=++log+%28k%29+%2F+a
y%5Eb++=+k+ → log+%28y%29++=++log+%28k+%29%2F+b
x%5Ec++=+t+
y%5Ed++=+t
So
k%2At=+x%5Ea%2Ax%5Ec+=+y%5Eb%2Ay%5Ed+=+x%5E%28a+%2B+c%29+=+y%5E%28b+%2B+d%29
then

%28a+%2B+c%29+log+%28x%29++=++%28+b+%2B+d%29+log%28+y%29
%28a+%2B+c%29%28log%28+k%29%2Fa%29++=++%28b+%2B+d%29%28log%28k%29%2Fb%29

%28a+%2B+c%29b++=++%28+b+%2B+d%29a
ab+%2B+bc++=+++ab+%2B+ad
[ bc+++=++ad+] → [ ad+++=++bc+]
answer: B) ad=bc