log4(little 4) 8

Question

how do i write this in y=?

Answer 1

Use the laws of logarithms,
log ab = log a+log b
log_aa = 1, and
log_a sqrt(b)=(1/2)log_a b
log 8
= log₄4*2
=log₄4+log₄2
=1+log_a2
=1+(1/2)log₄2
=1+(1/2)(1)
=3/2

Answer 2

Use the laws of logarithms,
log ab = log a+log b
log_aa = 1, and
log_a sqrt(b)=(1/2)log_a b
log 8
= log₄4*2
=log₄4+log₄2
=1+log₄2
=1+(1/2)log₄4
=1+(1/2)(1)
=3/2