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.
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