Question

Log(3)7 × log(4)81 × log(7)2

Answer 1

Log3 (7) * log 4 (81) * log7(2) 
= log 4 (7) * log 3 (81) * log7 (2) = 
= log 7 (7) * log3 (81) * log4 (2) = 
= 1 * 4 * 1/2 = 2 

Применил два раза 14 свойство

Answer 2

To evaluate the expression log(3)7 × log(4)81 × log(7)2, you can use the properties of logarithms, specifically the change of base formula:

log_b(a) = log_c(a) / log_c(b)

where log_b(a) represents the logarithm of a with base b, and log_c(a) and log_c(b) are logarithms with a common base c.

Let's apply this formula to your expression:

log(3)7 × log(4)81 × log(7)2

= (log(7) / log(3)) × (log(81) / log(4)) × (log(2) / log(7))

Now, simplify further:

= (log(7) / log(3)) × (2log(3) / 2log(2)) × (log(2) / log(7))

Notice that some terms cancel out:

(log(7) / log(7)) × (log(3) / log(3)) × (2 / 2)

= 1 × 1 × 1

So, the result is 1:

log(3)7 × log(4)81 × log(7)2 = 1