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 = log3 x

Accepted Answer

Hey everyone here we are asked to find the exponential form of six is equal to log base two of x. Now, before we can find the exponential form, we 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 from here we want to identify each of these variables from our given equation. So we can see that Y is equal to six, our base B is two and X is simply just X in both equations. And now from here we can towards finding the expert form, which if we recall the formula is B to the power of Y is equal to X. But before we can convert directly we need to meet a set of conditions. So we have to check that our X is greater than zero, our b is greater than zero and our B is not equal to one. So taking a look at our given equation, we see that X is just positive X. So it is greater than zero, B is positive two, so it is greater than zero and it is not equal to one. Therefore we know that our logarithmic form is equivalent to the exponential form. So we now can plug in our given values for the exponential form. So we have B which is two to the power of Y, which is six is equal to X, which is just X. Therefore we are left with answer choice C. Where we have the exponential form of two to the power of six 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 = log3 x

Key Concepts

Logarithmic Functions

Exponential Form

Base of a Logarithm

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