Question

Log 81/8+2log2/3-3log3/2+log3/4

Answer 1

The value of (log 81/8 + 2 log 2/3 - 3 log 3/2 + log 3/4) is 0.

• log 81/8 + 2 log 2/3 - 3 log 3/2 + log 3/4

Using the property, log (a/b) = log a - log b, we get,

log 81 - log 8 + 2 (log 2 - log 3) - 3 (log 3 - log 2) + log 3 - log 4

= log 3⁴ - log 2³ + 2 log 2 - 2 log 3 - 3 log 3 + 3 log 2 + log 3 - log 2²

• Using the property, log aᵇ = b log a, we get,

4 log 3 - 3 log 2 + 2 log 2 - 2 log 3 - 3 log 3 + 3 log 2 + log 3 - 2 log 2

• Brining all log 3 terms together and all log 2 terms together,

4 log 3 - 2 log 3 - 3 log 3 + log 3 - 3 log 2 + 2 log 2 + 3 log 2 - 2 log 2

= 0 (All log 3 terms and log 2 terms get cancelled)

Answer 2

Answer:

Using the property, log (a/b) = log a - log b, we get,

log 81 - log 8+ 2 (log 2 - log 3) - 3 (log 3 - log 2)+log 3-log 4

= log 34 - log 23 + 2 log 2 - 2 log 3-3 log 3+

3 log 2+ log 3-log 22

Using the property, log ab = b log a, we get, 4 log 3-3 log 2 + 2 log 2-2 log 3 - 3 log 3 +

3 log 2+ log 3 - 2 log 2

• Brining all log 3 terms together and all log 2 terms together,

4 log 3-2 log 3 - 3 log 3+ log 3 - 3 log 2 + 2 log 2+3 log 2-2 log 2

= 0 (All log 3 terms and log 2 terms get

cancelled)