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question 6

let ( b > 0 ).

( log_b(b) = b )

(circ) true
(circ) false

Explanation:

Step1: Recall the logarithm definition

By the definition of a logarithm, for \( b>0, b
eq1 \), \( \log_{b}(x)=y \) is equivalent to \( b^{y}=x \).

Step2: Apply the definition to \( \log_{b}(b) \)

Let \( y = \log_{b}(b) \). Then by the definition, \( b^{y}=b \). Since \( b>0 \), we know that \( b^{1}=b \), so \( y = 1 \). But the equation given is \( \log_{b}(b)=b \), which would mean \( 1 = b \) for all \( b>0 \), which is not true (e.g., if \( b = 2 \), \( \log_{2}(2)=1
eq2 \)).

Answer:

False