Question

Express the following as a single logarithm:

2 log 5 + 3 log 2 – 1

Answer 1

Given: 2 log 5 + 3 log 2 – 1

Step-wise calculation:

1. Use power rule:

2 log 5 = log (5²)

And 3 log 2 = log (2³)

2. Convert the constant:

1 = log 10

So –1 = –log 10.

3. Combine using product and quotient rules:

log (5²) + log (2³) – log 10 

= log (25) + log (8) – log (10) 

= log (25 × 8) – log (10) 

= log (200) – log (10) 

= `log (200/10)` 

= log (20)