Question

Use the change of Base formula to evaluate log5 92 . then convert. Log5 92 to a logarithm in base 3. Round to the nearest thousandth.

Answer 1

change of base is

`log_a(b)= (log_c(b))/(log_c(a))`
change base to 3

`log_5(92)= (log_3(92))/(log_3(5))`
why would you want base 3? base 10 is on most calculators
anyway, the value would be 2.809555

Answer 2

`\log_5 92=2.809`

`\log_3 2.809=0.940`

Explanation:

Given : Expression
`\log_5 92`

To find : Use the Change of Base Formula to evaluate the expression also convert the expression to a logarithm in base 3?

Solution :

Applying the change of Base Formula,

i.e.
`\log_b x=(log_a x)/(\log_a b)`

We get,

`\log_5 92=(\log 92)/(\log 5)`

`\log_5 92=(1.963)/(0.698)`

`\log_5 92=2.809`

So, The expression is
`\log_5 92=2.809`

Now, converting the expression to a logarithm in base 3.

Taking log base 3 in 2.809,

`\log_3 2.809=(log 2.809)/(\log 3)`

`\log_3 2.809=(0.448)/(0.477)`

`\log_3 2.809=0.940`

Therefore, The solution is
`\log_3 2.809=0.940`