Express as a single logarithm.

Question

1/2 log base b of (x-2)- log base b of y + (3 log base b of z) = log base 6 of (x-2)^1/2

Answer 1

(1/2) log_b(x-2) - log_by + 3log_bz = log₆(x-2)^(1/2)

log_b [ (x-2)^(1/2) z/y] = log₆(x-2)^(1/2)

log_b ( (z/y)√(x-2) ) = log₆ √(x-2)

are you sure the right side was not supposed to be
log_b ?

Answer 2

oops, didn't notice the 3 coefficient until I checked the display of this post.

should have been: z^3 in the last two lines.

log_b (x^3/y)log_b(x-2) = log₆ √(x-2)