Question

Solve the logarithm. (1/5)^(x-1)=(1/2)^(3-x)

Answer 1

take log of both sides, then put exponent out front

--> (x-1)log(1/5) = (3-x)log(1/2)

Answer 2

then combine x terms on one side

--> xlog(1/5) + xlog(1/2) = 3log(1/2) + log(1/5)

Answer 3

Factor out the x, then divide

--> x = [3log(1/2) + log(1/5)] /[ log(1/5) + log(1/2)]

Answer 4

Another person told me the answer was x= ln(40)/ln(10) ? Does that make sense to you??

Answer 5

yes just a matter of combining the logs

3log(1/2) + log(1/5) = log(1/2^3 * 1/5) = log(1/40) = -log(40)

log(1/2) + log(1/5) = log(1/2*1/5) = log(1/10) = -log(10)

Answer 6

Okay! Got it. Thank you!

Answer 7

yw