Question

+
Find
ind th
the
log(36) log
pogled
(36)
l
2​

Answer 1

Answer:

( log 2 + log 3 )

Step-by-step explanation:

To write this expression in terms of  log 2  and  log 3

you first have to write number  36

as a product of powers of  2  and  3 .

36 = 6 2

= ( 2 ⋅ 3 ) 2

So you can write:

log 36 = log ( 2 ⋅ 3 ) 2

Now you can use the properties of logarithms which say that:

log  a b = b ⋅

log a log ( a ⋅ b )

= log a + log b

After using rule  1

you get: log ( 2 ⋅ 3 ) 2

= 2 ⋅ log ( 2 ⋅ 3 )

Now if you use rule  2

you get the final result:

2 ⋅ log ( 2 ⋅ 3 )

= 2 ⋅ ( log 2 + log 3 )

Now you can write the final answer:

log 36 = 2 ⋅ ( log 2 + log3 )

Hope this helps