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Working out 'x' using Logarithms?
Hey guys and gals; Stuck on some logarithm questions, if you can help me out then it would be much appreciated, and if you can even help me out by going as far as explaining how you got the answer that would be even better! I'm trying to do them using a calculator too.
The questions are
8 to the power of (x+3). =24.5
and
6.5 to the power of x. =8.4 to the power of (4x-10)
Any help would be appreciated
1 Answer
- billrussell42Lv 79 years agoFavorite Answer
you could tell us what the actual question is. My guess is: solve for x.
8^(x+3) = 24.5
take log base 8 of both sides
log₈8^(x+3) = log₈24.5
rules of logs
(x+3)log₈8 = log₈24.5
(x+3) = log₈24.5
x = log₈24.5 – 3
x = 1.538 – 3 = –1.462
6.5 to the power of x. =8.4 to the power of (4x-10)
6.5^x = 8.4^(4x–10)
log base 10 both sides
log (6.5^x) = log(8.4^(4x–10))
x log 6.5 = (4x–10) log 8.4
(4x–10) / x = (log 6.5) / (log 8.4) = 0.813 / 0.924 = 0.880
4x – 10 = 0.880 x
x(4–0.880) = 10
x = 3.205
