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प्रश्न
Express the following as a single logarithm:
2 log 3 + log 7 + 3 log 5 – 2
योग
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उत्तर
Given: 2 log 3 + log 7 + 3 log 5 – 2
Step-wise calculation:
1. 2 log 3 = log (32) = log 9
2. 3 log 5 = log (53) = log 125
3. –2 = –log 100
4. Combine:
log 9 + log 7 + log 125 – log 100
= log (9 × 7 × 125) – log 100
= `log ((9 xx 7 xx 125)/100)`
5. Compute numerator:
9 × 7 × 125 = 7875
So expression = `log (7875/100)`
6. Simplify the fraction:
`7875/100`
= `(7875 ÷ 25)/(100 ÷ 25)`
= `315/4`
`log (315/4)`, which is equal to log 78.75.
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