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

Question

In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log9 x

Accepted Answer

Hey everyone here we are asked to find the exponential form of eight is equal to log base four of x. And now here we can see our given equation is in the logarithmic form. So before we can find the exponential form, we first need to identify that the logarithmic formula is why is equal to to log base B of X. And now we need to identify each of these variables from the formula in relation to our given equation. So we can see that Y is equal to eight, our base B is equal to four and X is simply equal to X. And now from here we need to recall the exponential form which is B to the power of Y is equal to X. And now before we can convert directly from log rhythmic to exponential forms, we need to ensure that the required conditions are met. So we need to check that X is greater than zero, B is greater than zero and B is not equal to one. And so looking at X, we see that it is positive X. So it is greater than zero. So this condition is met, next B is positive for, so it is greater than zero and is not equal to one. And now we can see all of our conditions are met, which tells us that the logarithmic form is the equivalent to the exponential form. So we can now plug in our values directly into the exponential form to convert the given equation. So now we have B which is four to the power of Y which is eight is equal to X. And that is our final answer here of answer choice D. Where the exponential form is four to the power of eight is equal to X. 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. 2 = log9 x

Key Concepts

Logarithmic Functions

Exponential Form

Base of a Logarithm

Watch next