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Given the graph of the logarithmic function below, determine the equation in the form f(x) = k + logbx.

b=?
k=?

Given the graph of the logarithmic function below, determine the equation in the form-example-1

1 Answer

5 votes

Answer:


f(x)=1+log_(2)(x)

Explanation:

The given function is
f(x)=k+log_(b)(x), and we know some points such that f passes through them, like (1,1) and (2,2). then we can get the next equations:


f(1)=1=k+log_(b)(1)\\

but
log_b(1)=0\\ given that
b^0=1 for any number b, then:


1=k+0=k

Similar, we can take the point (2,2):


2=f(2)=1+log_b(2)\\1=log_b(2)\\b^1=2\\b=2\\

The last equalities are given by definition of logarithm

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