Name: karim

Question:
Find the Domain of the Function
H(x) = Log3 (4x + 7)-10
H(x) = log base 3 times 4X plus 7 minus 10
i am having problem solving these kinds of problems.

Hi Karim,

I am going to simplify my typing by typing h for H(x).

If h = log₃(4x + 7) - 10 then h + 10 = log₃(4x + 7). Now think about what log₃ is.

y = log₃(s) means that 3^y = s

Thus

h + 10 = log₃(4x + 7) means that 3^{h + 10} = 4x + 7

The important fact to notice here is that, depending on the value of h, 3^{h + 10}can be any positive real number, but it can't be zero or negative. Thus

4x + 7 > 0,

that is

x > ^-7/₄

Thus the domain of H(x) is {x | x > ^-7/₄}

Penny

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