SOLUTION: evaluate without using a calculators or tables log 0.7 power 1

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Question 348525: evaluate without using a calculators or tables
log 0.7 power 1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the problem is:
log%280.7%2C+%281%29%29
If so, this is called the "base 0.7 logarithm of 1"

To find this logarithm without calculators or tables, you have to understand what logarithms are. In short, logarithms are exponents. Specifically, log%280.7%2C+%281%29%29 represents the exponent for 0.7 that results in 1. So we have to ask ourselves: "What power of 0.7 is 1?". With some thought and with some understanding of how a certain exponent works, we can answer this question. The exponent for 0.7 (or for any non-zero number for that matter) that results in a 1 is ... Zero! Any number (except zero itself) raised to the zero power is 1! So:
log%280.7%2C+%281%29%29+=+0

In fact
log%28a%2C+%281%29%29+=+0
for any positive number!