If log 8 = 3, how to find the value of log 32

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Given log8 = 3.

To find log 32.

Solution:

log8 = 3.

8 = a^3 where a is the base of log.

So a = 2 is the base of log.

32 = 2^5.

32 = 2^5

log2 (32 )= log 2 (2^5) = 5.

So if log8 = 3, then log32 =5.

We are given that log 8 = 3. Here the base of the logarithm is not mentioned.

For a logarithm with the base b, if log(b) a =c it follows that a = b^c.

We use this relation here, let the base of the logarithm be n.

Therefore log(n) 8 = 3

=> 8 = n^3

=> 2^3 = n^3

Hence n is 2. Now we now the base of the logarithm is 2.

Therefore log (2) 32 = log (2) 2^5 = 5.

**The value of log 32 is 5.**

Let:

a = base of the log

Then the equation log 8 = 3 implies:

a^3 = 8

Therefore:

a = 8^(1/3) = 2

We know:

32 = 2^5

Therefore:

log 32 = 5

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