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March 30, 2017

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3ln(b) + 2ln(c)

write as a single log.

I have tried this problem so many ways. i don't know what to do with the 3 and the 2. do you multiply or use them as exponents or what

  • Math - ,

    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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