Question

2 log 2 – 3 log 3 + 4 log 4 = ______

Options

• `1024/27`

• `log  4/(27 xx 256)`

• `log  1024/27`

• `4/(9 xx 256)`

Answer 1

2 log 2 – 3 log 3 + 4 log 4 = `underlinebb(log  1024/27)`

Explanation:

2 log 2 – 3 log 3 + 4 log 4

Step 1: Apply the logarithmic power rule:

log aⁿ = n log a

So,

log 2² – log 3³ + log 4⁴

log 4 – log 27 + log 256

Step 2: Combine the logarithms:

Using rules:

log a + log b = log (ab), log a – log b = `log (a/b)`

= `log((4 xx 256)/27)`

= `log  1024/27`