What is the Correct Characteristic for log15 850?

[nvez]

Hello,

I understand the current concept of the characteristic however there either is a mistake in my answerbook or I made a mistake

log₁₅ 850 = 850^(1/15) = 1.568

The characteristic should be 1 and the mantissa is 0.568 -- My answer book says it's 2. I have done all my other exercices and they were correct, just wondering if this is an exception (different concept because base > 10?)

Thanks in advanced.

 

[Mark44]

Hello,

I understand the current concept of the characteristic however there either is a mistake in my answerbook or I made a mistake

log₁₅ 850 = 850^(1/15) = 1.568

The value for the characteristic in your book is right. Both expressions to the right above are wrong.
log₁₅ 850 is not the 15th root of 850.
Think about the basic definition of the logarithm base whatever. By definition,
log_a b is the exponent on a that produces b.
IOW, if log_a b = N, then a^N = b.

For your problem, log₁₅ 850 has to be somewhere between 2 and 3, since 15^2 = 225 < 850 < 3375 = 15^3.

Obviously you are not going to be able to evaluate the expression directly using a calculator.

Let log₁₅ 850 = L. Now rewrite this log equation as an exponential equation, and then take the log of both sides in some more convenient base so that you can solve for L.

The characteristic should be 1 and the mantissa is 0.568 -- My answer book says it's 2. I have done all my other exercices and they were correct, just wondering if this is an exception (different concept because base > 10?)

Thanks in advanced.

 

[nvez]

log₁₅ 850 is not the 15th root of 850.
Think about the basic definition of the logarithm base whatever. By definition,
log_a b is the exponent on a that produces b.
IOW, if log_a b = N, then a^N = b.

That was my problem! I got it all figured out now.

Thank you very much! I appreciate your help and your dedicated time to this!