Question

Express the following as a single logarithm:

2 log 3 + log 7 + 3 log 5 – 2

Answer 1

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.