What is the base 5 representation of the number 465^8

We need to convert given value 465^8 as the base 5 number.

Let us assume x is the exponent of 5 when we take base 5.

We can setup an equation now.

5^x=465^8

Taking ln on both sides, we get

On simplifying, we get

Therefore, .

Step-by-step explanation:

Let

Now we take log on both the sides of the equation.

log(x) =

Now to get 5 as the base we will divide this equation by log5 on both the sides.

=

=

= 30.57

Therefore, base 5 representation of the given number will be