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

Question

In Exercises 1–8, write each equation in its equivalent exponential form. log6 216 = y

Accepted Answer

Hey everyone here we are asked to find the exponential form of log base five of 125 is equal to why. And now here we need to note that our given equation is in the general logarithmic form which if we recall is the formula log base B of X is equal to y. So we want to begin by identifying each of these variables from the formula in relation to our given equation. So we can see that B is the base which is equal to five. We then have X, which is equal to 125 and why is simply just why? And now from here we want to work towards converting to the exponential form which if we recall is B to the power of Y is equal to X. However, we can't directly convert without first making sure that we meet the required condition which are X must be greater than zero, B must be greater than zero and B cannot be equal to one. And as long as all of these conditions are met, we know that the long rhythmic form is equivalent to this exponential form. So now we can check our given equation and we see that X is 125 which is greater than zero. So this condition is met, B is equal to positive five, which is greater than zero and not equal to one. So now we can see all of our conditions are met and we can go ahead and plug in our values directly into the exponential form. So we have B which is five to the power of Y, which is just Y. Is equal to X, which we have as 125. So we are left with answer choice C, where we have five to the power of Y is equal to 125. 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. log6 216 = y

Key Concepts

Logarithms

Exponential Form

Base of a Logarithm

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