The logarithmic function f(x)=logbx𝑓(𝑥)=log𝑏⁡𝑥 can also be written in exponential form as:Question 6Select one:a.y=bx𝑦=𝑏𝑥b.x=by𝑥=𝑏𝑦c.b=yx𝑏=𝑦𝑥d.b=xy

To convert the logarithmic function $f(x) = \log_b x$ into its exponential form, we need to understand the relationship between logarithms and exponents.

1. Break Down the Problem

   We have the logarithmic form $f(x) = \log_b x$. We need to convert this into its exponential form.

2. Relevant Concepts

   The definition of logarithms states that if $y = \log_b x$, then $b^y = x$. This means that the base $b$ raised to the power $y$ equals $x$.

3. Analysis and Detail

   • Start with the given logarithmic function: $y = \log_b x$.
   • Apply the definition of logarithms: We can rewrite this as $b^y = x$.

4. Verify and Summarize

   • Therefore, the correct exponential form of the logarithmic function $f(x) = \log_b x$ is $x = b^y$.
   • This matches option b: $x = b^y$.

Final Answer

The correct answer is b. $x = b^y$.