If 3logA base 2 is equal to B and log 4A is equal to B plus 4 where A and B are numbers .

Question

this is a question under logarithm. if 3 log A base 2 is equal to B and log 4 A is equal B plus 4 where A and B are real numbers , find the values of A and B

Answer 1

3log₂(A)=B, log₂(4A)=B+4.

log₂(A³)=B, A³=2^B;

2+log₂(A)=B+4, log₂(A)=B+2, A=2^B+2.

A³=2^B=2^3B+6, B=3B+6, 2B=-6, B=-3,

A=2^-3+2=2^-1=½.