In Exercises 13–15, write each equation in its equivalent exponen...

Question

In Exercises 13–15, write each equation in its equivalent exponential form. 1/2 = log49 7

Accepted Answer

Hello. Today we're going to rewrite a logarithmic equation into an exponential form. So the logarithmic equation given to us is the logarithms of base 216 with argument six equal to 1/3. Now, in order to rewrite this into an exponential equation, let's go ahead and recall one of our logarithmic rules. So we have a logarithmic rule that states that if we have the log base of a with an argument be equal to see this statement could be rewritten as a race to the power of C equal to be. So all we've done is taken this argument of this base of a, raise it to the power of C and set it equal to B. That's how we end up with this exponential statement. So in this case here we're gonna take 216, raise it to the power of a third and set it equal to six. Doing so is going to give me 216 raised to the power of 1/3 equal to six. And this is gonna be the exponential form of this logarithmic equation. That also means that the solution to this problem is going to be a. So I hope this video helps you in understanding how to rewrite logarithms into exponential forms and I'll go ahead and see you all in the next video

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In Exercises 13–15, write each equation in its equivalent exponential form. 1/2 = log49 7