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How do you simplify #ln 3 − 2 ln(8 + 7)#?

Answer 1

Sadie Alexander

-ln 75

The given expression is ln 3 -2 ln 15

=ln 3 - ln #15^2#

= ln3 -ln 225

= ln #3/225#

= ln #1/75#

=ln #(75)^-1#

= -ln 75

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Answer 2

James Allen

To simplify ln(3) - 2ln(8 + 7), apply the properties of logarithms:

Use the property ln(a) - ln(b) = ln(a/b) to simplify ln(3) - ln((8 + 7)^2).
Simplify ln(3) - ln(225).
Use the property ln(a) - ln(b) = ln(a/b) again to simplify ln(3/225).
Simplify ln(1/75).

So, ln(3) - 2ln(8 + 7) simplifies to ln(1/75).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.