Question

Which equation is equivalent to 16^2p=32^p+3

Answer 1

Answer with explanation:

The equation given is

`(16)^(2p)=(32)^(p+3)\\\\(2^4)^(2p)=(2^5)^(p+3)\\\\2^(8p)=2^(5p+15)\\\\ \text{equating power of ,2}\\\\ 8p=5p+15\\\\8p-5p=15\\\\3p=15\\\\p=(15)/(3)\\\\p=5\\\\ \text{Used following law of exponents}\\\\x^(ma)=(x^m)^a`

Answer 2

`16=2^4\\\\32=2^5\\\\\text{Use:}\ (a^n)^m=a^(n\cdot m)\\\\16^(2p)=32^(p+3)\\\\(2^4)^(2p)=(2^5)^(p+3)\\\\2^(4\cdot2p)=2^(5\cdot(p+3))\\\\2^(8p)=2^(5p+15)\iff8p=5p+15\ \ \ |-5p\\\\3p=15\ \ \ \ |:3\\\\p=5`