Question

Solve the equation 1296^x = 6

Answer 1

you can also write it as \[\log_{1296}6 = x\] and you can have a nice guess that the no. 1296 is a square of something as 6 is the last digit, since 6 comes in the squares of 4 and 6 you'll have an accurate guess. now since (30)^2 is less than 1200 and (40)^2 is more than 1200 we now know that the no. lies somewhere inside the 30 and 40. We can either guess 34 or 36. you can calculate that right? Ok now we know 36^2 = 1296 so 6^4 = 1296. therefore,\[1/4 \log_{1296}1296 = x\]\[1/4*1 = x\]since the log with the same no. and base is 1. x=1/4

Answer 2

One way to answer this is using logarithms. If you take the logs of both sides then you have \[\log (1296^x) = \log (6)\] Now logs have a couple of special rules, one of which is \[\log (a^b)=b \times \log (a)\] Using this rule we have \[x \log (1296)=\log(6)\] which if we rearrange gives\[x=\frac{\log(6)}{\log(1296)}=0.25\]

Answer 3

Thank you both very much

Answer 4

Glad to help :)

Answer 5

you're welcome :) and helen's method is also great ^^