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Need help with these two questions please

Need help with these two questions please-example-1

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Answer:

  1. B, D, F, G
  2. 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.

__

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

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