Question

Condense to a single logarithm: ln x +ln y − z

Question 1 options:


A)


ln xy∕ ln z



B)


(ln x)(ln y∕z)



C)


ln xy∕z


D)


ln (x + y – z )

Answer 1

ln(xy/z)

Explanation:

Answer 2

The correct condensed logarithmic expression is ln(xy/z). So option C is correct.

I assume the x term should be part of a natural log, ln(z), due to if it isn't none of the answer choices would be correct.

We can use two logarithmic simplifying rules.

logA + logB = log(A*B)

logA - logB = log(A/B)

Using this, we add ln(x) and ln(y) so xy will be multiplied, while the z will be divided due to it being subtracted.

ln(x) + ln(y)= ln(xy)

ln(xy) - ln(z) = ln(xy/z)