Answer:
- B, D, F, G
- D
Explanation:
1.
The true statements more or less speak for themselves.
The only value that has the same log for different bases is log(1) = 0 = ln(1). This means the first statement (A) is false.
The inverse function of y = e^x is found by swapping x and y:
x = e^y
Taking natural logs of this equation gives you ...
ln(x) = y
Hence the equations of B are, in fact, inverses.
Statement D is true, rendering statement C false.
The expressions in statement E are, in fact, equivalent, rendering E false.
Statement F shows the meaning of ln( ).
Statement G is a restatement of B. If two functions are inverses, their composition is x, the original argument.
The true statements are B, D, F, G.
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2.
The relevant rules of logarithms are ...
log(a^b) = b·log(a)
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
Using these rules on the given expression, we have ...
ln(x^4y/z) = ln(x^4y) -ln(z) = ln(x^4) +ln(y) -ln(z)
= 4ln(x) +ln(y) -ln(z) . . . . . matches choice D