Problem

Write the following logarithmic equation as an exponential equation. Do not simplify your answer. \[ \log _{b}(3.9)=5 \] Answer 2 Points Keypad Keyboard Shortcuts

Solution

Step 1 :The logarithmic equation given is \(\log _{b}(3.9)=5\).

Step 2 :We can convert this logarithmic equation to an exponential equation using the property of logarithms that states: if \(\log_b(a) = c\), then \(b^c = a\). Here, \(b\) is the base, \(a\) is the argument of the logarithm, and \(c\) is the value of the logarithm.

Step 3 :So, we can rewrite the given logarithmic equation \(\log_b(3.9) = 5\) as an exponential equation \(b^5 = 3.9\).

Step 4 :The exponential form of the given logarithmic equation is \(\boxed{b^5 = 3.9}\).

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