how you do the second problem?

It's been a long time since high school and english isn't my native language so I'm sure my answer will be hard to understand or incorrect, but:

log(1/2)5 means you're looking for the x that solves (1/2)^x = 5

the bigger x gets the smaller (1/2)^x gets starting from 1/2 towards 0 so the answer is clearly not a positive number

negative exponent transforms the equation to -> 1/(0.5^x) = 5

0.5^1 = 0.5 so with x = 1 we have 2, with x = 2 -> 4, with x = 3 -> 8, etc

so the answer is -2.3219

They wanted you to use the log base change rule.

Log a X = log b X / log b a

log (5) / log (0.5)

based on how the problem is worded, i think they want you to use the change of base formula (posted above), then change it to a log base your calculator can handle (log base 10), then use the calculate to get the estimate.

we can say log base 1/2 of 5 is equal to x if
(1/2)^x = 5. Make this 2^(-x) = 5 <------ nothing is changed here, just changed (1/2)^x to 2^(-x)
now take ln of both sides to get
-xlog(1/2) = log(5)
thus -x = log(5)/log(1/2) = -2.3219
divide by -1 to get x=2.3219

This post was edited by ringo794 on Jun 23 2016 07:05pm

yall so smart

And you can finally check that (1/2)^-2.32... ~ 5