Question 1139360: log3 x = m can you please tell how solve this question??
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! log3(x) = m if and only if x = 3^m.
your solution would be x = 3^m.
if so, then log3(3^m) = m would have to be true.
you should be able to take any value of m and show that this is true.
for example, log3(3^5) should be equal to 5.
since log3(3^5) is equal to 5 * log3(3) and since log3(3) = 1, then you get 5 = 5, which is true.
another way to confirm is to use the log base conversion formula and solve using your calculator.
the log base conversion formula says that logb(x) = logc(x) / logc(b).
if b is equal to 3 and c is equal to 10, this becomes log3(x) = log10(x) / log10(3).
since log10 is the log function of your calculator, then you get log3(x) = log(x)/log(3).
when x = 3^5, this becomes log3(3^5) = log(3^5) / log(3).
you use your calculator to get log(3^5) / log(3) = 5.
you can also see thqt log3(3^5)) = log(3^5) / log(3), and swince log(3^5) is equal to 5 * log(3), this becomes log3(3^5) = 5 * log(3) / log(3) which is equal to 5 * 1 which is equal to 5.
i'm not exactly sure what else you can do with this.
the basic property of logs says that logb(x) = y if and only if x = b^y.
when b = 3 and y = m, this becomes log3(x) = m if and only if x = 3^m.
that's what we started with above.
some basic properties of logs are:
logb(x) = logc(x) / logc(b)
we used this one above.
log(x^a) = a * log(x)
we used this one above.
logb(b) = 1.
i think we used this one above as well.
you can confirm this one for base of 10 using the log function of your calculator, i.e. log(10) will be equal to 1.
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