Question 139875: These problems are froma a sample final, not a text book.
question #1 - 9^2x = 5^3x-4 solve equation
question #2 - log(base 5)e - use change of base formula
question #3 - log (base 2)(a^2 sqrt b^3)^4 write as summ/differ of log,express powers as factors
question #4 - ln(9-x^2) - find domain
I am studying my sample final...finals coming soon, these 4 problems are giving me trouble...ANY HELP WOULD BE GREATLY APPRECIATED!!!!
exponetial and logaarithmic problems are giving me major pproblems.
Thanks again for all your help!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! question #1 - 9^(2x) = 5^(3x-4) solve equation
Take the log of both sides:
2xlog9 = (3x-4)log5
xlog81 = 3xlog5 -4log5
xlog81 = xlog15^3 - log5^4
x(log81-log15^3) = log5^4
x = log5^4/(log81 -log15^3)
x = -1.7261
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question #2 - log(base 5)e - use change of base formula
log5 e = lne/ln5 = 1/ln5 = 0.62133...
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question #3 - log (base 2)(a^2 sqrt b^3)^4 write as summ/differ of log,express powers as factors:
log (base 2)(a^2 sqrt b^3)^4 = log2 (a^8 b^2)= 8log2 a + 2log2 b
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question #4 - ln(9-x^2) - find domain
9-x^2 > 0
x^2 < 9
-3 < x < 3
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Domain: All Real numbers except -3 < x < 3
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Cheers,
Stan H.
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