if log 125 to the base b is equals to C then Log 25 to the base b is what percent of the value of c
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Given: log(base b) 125 = c
To find: Log 25(base b) is what percent of the value of c?
Solution:
- Now we have given:
log(base b) 125 = c
log(base b) (5 x 25) = c
- Now we know the property log (ab) = log a + log b
- Applying this, we get:
log(base b) 5 + log(base b) 25 = c
log(base b) 5 + log(base b) 5² = c
- Now we know the property log a^m = m log a
- Applying this, we get:
log(base b) 5 + 2 log(base b) 5 = c
3 log(base b) 5 = c
log(base b) 5 = c/3
- So from this, we have:
log(base b) 25 = 2 log(base b) 5 = 2c/3
- So percentage is:
2/3 x 100 = 66.67 %
Answer:
Log 25(base b) is what 66.67% of the value of c.
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