SOLUTION: Given that loga2 = 0.693 and loga7 = 1.946, evaluate loga2/7.

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Question 1040597: Given that loga2 = 0.693 and loga7 = 1.946, evaluate loga2/7.
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Given that loga2 = 0.693 and loga7 = 1.946, evaluate loga2/7.
:
log%28a%2C%282%2F7%29%29 can be expanded to
log%28a%2C%282%29%29 - log%28a%2C%287%29%29
therefore
.693 - 1.946 = -1.253
log%28a%2C%282%2F7%29%29 = -1.253
:
We can evaluate a
The exponent equiv
a%5E-1.253 = 2%2F7
using common logs
log%28%28a%5E-1.253%29%29 = log%28%282%2F7%29%29
-1.253log%28%28a%29%29 = -.5441
log(a) = -.5441%2F-1.253
log(a) = .4342
Find the antilog
a = 2.717
:
:
Check using log%28a%2C%282%29%29+=+.693
log%282.717%2C%282%29%29+=+.693
2.717%5E.693 = 1.999 ~ 2


Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
.
On properties of logarithms see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
in this site.