SOLUTION: Given log2 T - log4 V = 5, express T in terms of V.

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Question 881828: Given log2 T - log4 V = 5, express T in terms of V.
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you can use the log base conversion formula to solve this.
that formula is:
loga(x) = logb(x) / logb(a)
from this formula, you get:
log4(v) = log2(v) / log2(4)
since log2(4) is equal to 2, this becomes:
log4(v) = log2(v) / 2
the original equaiton is:
log2(t) - log4(v) = 5
replace log4(v) with log2(v)/2 and you get:
log2(t) - log2(v)/2 = 5
multiply both sides of this equation by 2 to get:
2 * log2(t) - log2(v) = 10
since 2 * log2(t) is equal to log2(t^2), you get:
log2(t^2) - log2(v) = 10
since log2(t^2) - log2(v) = log2(t^2/v), you get:
log2(t^2/v) = 10
this is true if and only if 2^10 = t^2/v
multiply both sides of this equation by v to get:
t^2 = 2^10 * v
take the square root of both sides of this equation to get:
t = +/- sqrt(2^10 * v)

your possible solutions are t = +/- sqrt(2^10*v)
i checked it out as best i could and the answer looks good for t = + sqrt(2^10*v).
i don't believe it's good for t = -sqrt(2^10*v) because log2(t) would then be taking the log of a negative number which is not allowed if you are looking for a real solution.