Question

expand the logarithm as a sum or difference and or contant multiple of logarithms

log _4 16xy^2

thank you.. I know you do this:
log _4 16+ log _4 (x)+ log _4 (y^2)
and I know the first part = 2 and the last part you use the exponent rule =y^2log4
but the middle i don't get..thanks

Answer 1

For the last part of log₄ (y^2)
you follow the pattern of

log_a (x^n)
= n log_a x

so log₄ (y^2)
= 2 log₄ y

the first part of your solution is ok

final answer:
2 + log₄ x + 2 log₄ y

Answer 2

love you guys