Question

HELLLLLPPPPP

Condense the expression to the logarithm of a single quantity.
3 ln(5) + 2 ln(z – 6)

Answer 1

Hi! I actually created a tutorial on this topic. Check out the link below:

http://chilimath.com/advanced%20algebra/log/log-condensing.html

Answer 2

What I would do first is to bring that coefficient to the left of "ln" as exponents of the terms inside the parenthesis.

Answer 3

So it should look something like this...

\[\ln(5)^3+\ln(z-6)^2\]

Answer 4

Now, apply the rule in condensing logarithm whenever you see addition between them.

\[\ln(x)+\ln(y)=\ln(xy)\]

In other words, the sum of their ln's equals the ln of the product of the terms.

Answer 5

Finally, simplify it further to get the final answer as...

\[\ln(5)^3+\ln(z-6)^2=\ln[(5^3)(z-6)^2]=\ln[125(z-6)^2]\]