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

Question

In Exercises 1–8, write each equation in its equivalent exponential form. 4 = log₂ 16

Accepted Answer

Hey everyone here we are asked to find the exponential form of three is equal to log base three of 27. And now before we can find the exponential form, we first need to note that our given equation is in the logarithmic form, which if we recall the formula is why is equal to log base B of X. And now with this we want to identify each of these variables in relation to our given equation. So we see that Y is equal to three, our base B is equal to three and our X is equal to 27. And now from here we should recall the exponential form which is B to the power of Y is equal to X. And now, before we can convert directly from the logarithmic form to the exponential form, we need to meet a set of conditions. So these conditions are X must be greater than zero, B is greater than zero, and B cannot be equal to one. And so with this let's check our given equation. So our X is positive 27. So we can see that it is greater than zero. So this condition is met. Now we have positive three for B which is greater than zero and it is not equal to one. And so now all of our conditions are met. So we know that the logarithmic form is equivalent to the exponential form. So all we have to do is plug in our values into the exponential form. So for B we have three to the power of Y, which is three is equal to X, which is 27. And that leaves us with answer choice. A 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. 4 = log₂ 16

Key Concepts

Logarithms

Exponential Form

Base of a Logarithm

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