Posted by **Diana** on Friday, March 2, 2012 at 10:04am.

3ln(b) + 2ln(c)

write as a single log.

I have tried this problem so many ways. i dont know what to do with the 3 and the 2. do you multiply or use them as exponents or what

- Math -
**Brandon**, Friday, March 2, 2012 at 11:47am
Hello Diana,

Remember the three basic rules when dealing with logs:

n * log(A) = log(A^n)

log(A) + log(B) = log(A*B)

log(A) - log(B) = log(A/B)

Also note that log, and ln are both logarithms and interchangable, just with base 10 for log and base of nature exponent e for ln.

Using the above the logarithm can be easily reversed into a single logarithm.

Original Problem:

3 * ln(b) + 2 * ln(c)

Move logarithmic multiplication inside the log as exponents:

ln(b^3) + ln(c^2)

Convert addition into multiplication within the logarithmic function.

ln((b^3)*(c^2))

Since b and c are not the same base you cannot simplify any further.

Therefore the solution is:

ln((b^3)*(c^2))

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