In Exercises 1–8, write each equation in its equivalent exponenti...

Question

In Exercises 1–8, write each equation in its equivalent exponential form. 5= logb 32

Accepted Answer

Hey everyone here we are asked to find the exponential form of three is equal to log base B of 64. Now, before we refer to exponential form, we need to note that our given equation is in the general log arrhythmic form, which is if you recall why is equal to log base B of X. And now from here we just want to identify each of these variables in relation to our given equation. So we can see that Y is three, B is the base and B is just B. And then X is 64. And now from here we can work towards finding the exponential form, which if we rick call the exponential form is B to the power of Y is equal to X. And now we can't directly convert to the exponential form unless the required conditions are met. So we must have X is greater than zero. B also must be greater than zero, but B cannot be equal to one. And now we want to check our equation and see that all of these conditions are met. So we can see that X is 64, so it is greater than zero, B is just be, so it is positive, so it's greater than zero and it is not equal to one. So all of our conditions are met. So we can just plug in our values directly into the exponential form because we now know that it is equivalent to the logarithmic form. So we have B which is just B to the power of Y, which is three is equal to X, which we found to be 64. So that leaves us with the final answer of choice A. Where we have B to the power of three is equal to 64. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

In Exercises 1–8, write each equation in its equivalent exponential form. 5= logb 32

Key Concepts

Logarithmic Functions

Exponential Form

Change of Base Formula

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