stuck on algebra problem!!!?
which statements are correct for these functions?
y=log[10]x and y=log[e]x
a)the graphs have the same x- intercept
b) for all values of x, log[e]x are ≥ log[10]x
c) when x>1, both functions are positive
d) the functions have the same domain
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Verified answer
a) True n^0=1 for any real number n. Therefore, all logarithmic functions intersect the x-axis at x=1.
b) False if x= 1, log[e]x > log[10]x only for 0< x <1 see: http://www.wolframalpha.com/input/?i=ln%28x%29+vs+...
c) True (this is true for all real logarithms with a positive base) Short answer why, for a number with a positive base, no matter the exponent the sign doesn't change.
d) True, The domain is the set of all x values for which the function is defined. For all logarithmic functions, this is x > 0.
a , c , d