Answer:
[tex]log_{32}(2)=0.2[/tex]
Step-by-step explanation:
Recall that the unknown (x) here is the log base 32 of 2, so we can write this as the equation:
[tex]log_{32}(2)=x[/tex]
The above equation can be solved by the "change of base formula":
[tex]x=\frac{log(2)}{log(32)} \\x=0.2[/tex]
We can also answer this by trying to solve the exponential equation:
[tex]32^x=2[/tex]
Where we are asked what is the exponent (x) at which we need to raise the base (32) in order to obtain the answer "2"?
Notice that since
[tex]2^5=32[/tex]
Then [tex]32^{1/5} = 2[/tex]
And 1/5 = 0.2 which also agrees with our previous answer
