Video: Converting an Equation from Exponential to Logarithmic Form

Chris O’Reilly

Express (9/7)Β² = 81/49 in its equivalent logarithmic form.

01:38

Video Transcript

Express nine over seven all squared equals 81 over 49 in its equivalent logarithmic form.

Well, if we take a look at the question, we have nine over seven all squared is equal to 81 over 49. And this is actually an exponential form. And what we’re trying to do is actually converting into the logarithmic form. And to enable us to do that, we actually have a relationship. And that is that if we have in the exponential form π‘Ž to the power of 𝑐 is equal to 𝑏, then our equivalent logarithmic form is going to be log to the base π‘Ž of 𝑏 is equal to 𝑐.

And great, now that we have this relationship, what we can actually do is we can actually look at our exponential form in the question and actually find its equivalent logarithmic form. So if we look at our nine over seven all squared equals 81 over 49, then our π‘Ž is equal to nine over seven, our 𝑏 is equal to 81 over 49, and our 𝑐 is equal to two.

Okay, so now what we can do is we can actually substitute these values into our logarithmic form. So therefore, if we actually substitute these values in, we get log to the base nine over seven of 81 over 49 is equal to two.

So we’ve reached the final answer and we can say that nine over seven all squared equals 81 over 49, which is the exponential form. Well, its equivalent logarithmic form is log to the base nine over seven of 81 over 49 is equal to two.

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