In Exercises 9–20, write each equation in its equivalent logarith...

Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. 5^4 = 625

Accepted Answer

Hey, everyone here, we are asked to find the logarithmic form of three to the power of five is equal to 243. Now, first, before we find the logarithmic form, we need to note that our given equation is in exponential form. So first, we need to recall the exponential form which is B to the power of Y is equal to X. In next, we want to identify each of these variables from our given equation. So we can see that B is equal to three and three is to the power of five. So we see that Y is equal to five in next, it is equal to 243. So we can see that X is equal to 243. And next, we need to recall that X must be greater than zero, B must be greater than zero. And B cannot be equal to one in order for the exponential form to be equivalent to the general logarithmic form, which is log base B of X is equal to Y. So from here, we want to check that all of these conditions are met. So here our X is greater than zero. And so that statement is true B is three. So it's also greater than zero and it is not equal to one. So all of our conditions are met. So we can go ahead and convert our exponential form into the general logarithmic form. So we have log based B which we identified as three of X, which is 243 is equal to Y, which is five. And that is our final answer here. Of choice. B Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 9–20, write each equation in its equivalent logarithmic form. 5^4 = 625

Key Concepts

Exponential Form

Logarithmic Form

Change of Base Formula

Watch next