Question

2
Evaluate without using log table
log 5 power 8​

Answer 1

Answer:

not believe the poster intended to approximate any logarithm. – suneater Feb 15 '16 at 1:19

3

slide rule works for me... – Joel Feb 15 '16 at 10:03

@Joel he said without a calculator :-) – Matt Gutting Feb 15 '16 at 12:17

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To evaluate log8128log8⁡128, let

log8128=x

log8⁡128=x

Then by definition of the logarithm,

8x=128

8x=128

Since 8=238=23 and 128=27128=27, we obtain

(23)x23x=27=27

(23)x=2723x=27

If two exponentials with the same base are equal, then their exponents must be equal. Hence,

3xx=7=73

3x=7x=73

Check: If x=73x=73, then

8x=873=(813)7=27=128