For each step, the logs are all base b. This is to save time and hassle of writing tricky notation of having to write the smaller subscript 'b' multiple times. The first rule to use is that log(x^y) = y*log(x) for any base of a logarithm. The second rule is that meaning that the log base of itself is 1
log(b^(6x)) = 6x*log(b) .... pull down exponent using the first rule above
log(b^(6x)) = 6x*1 .... use the second rule mentioned
We will first calculate ∠A: ∠∠A = 180° - ( 105° + 20 ° ) = 180° - 125° = 55° Then we will use the Sine Law: 15 / sin 55° = AB / sin 20° 15 / 0.81915 = AB / 0.342 AB · 0.81915 = 15 · 0.342 AB · 0.81915 = 5.13 AB = 5.13 : 0.81915 AB = 6.26 ≈ 6.3 miles Answer: The distance between the locations A and B is 6.3 miles.