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

Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. 2^-4 = 1/16

Accepted Answer

Hey everyone here we are asked to find the logarithmic form of four. To the power of negative three is equal to one divided by 64. Now, before we can find the logarithmic form we need to note that our given equation is in exponential form. So we first need to recall the exponential form which is B to the power of why is equal to X. And now with this we want to identify each of these variables values. So starting with B, we see that B is four and four is to the power of negative three, so Y is negative three and that leaves us with X, which is equal to one divided by 64. And now from here we need to also recall that when X is greater than zero and B is greater than zero and B is not equal to one. That the exponential form is equivalent to the log base of B of X is equal to Y. So with this information we need to check that X is greater than zero which it is. And we also need to have B is greater than zero, B is four, so it's also greater than zero and B cannot be equal to one which it is not. So it needs all the conditions. So we can convert from this exponential form to the logarithmic form. So doing so we just need to plug in all of our values. So we have log base of B which is four of X, which is one 64th is equal to Y, which is negative three. And this is our final answer, which is answer choice D. 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. 2^-4 = 1/16

Key Concepts

Exponential Equations

Logarithmic Form

Properties of Logarithms

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