What is the Domain of the following logarithmic functions?
1) f(x) = log(3x - 21)
2) f(x) = log(2x + 16)
3) f(x) = log2 (x - 2)
Perform the operations:
4) log2 4 + log4 2 =
5) log 1000 + ln e5 =
6) log1/2 8 =
Solve the equations:
7) x2 = log 100 + 119
8) Solve the equation log 4 + log x = log 28
9) Solve the equation log (x + 3) + log x = log 28
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1) The domain of f(x) = log(3x - 21) is x > 7.
2) The domain of f(x) = log(2x + 16) is x > -8.
3) The domain of f(x) = log2 (x - 2) is x > 2.
4) log2 4 + log4 2 = 2 + 0.5 = 2.5.
5) log 1000 + ln e5 = 3 + 5 = 8.
6) log1/2 8 = -3.
7) x^2 = log 100 + 119 is not a solvable equation. (There may be a typo)
8) log 4 + log x = log 28
log (4x) = log 28
4x = 28
x = 7.
9) log (x + 3) + log x = log 28
log (x^2 + 3x) = log 28
x^2 + 3x = 28
x^2 + 3x - 28 = 0
(x + 7)(x - 4) = 0
x = -7 or x = 4.
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