Video: Converting an Equation from Exponential to Logarithmic Form

Express (0.7)³ = 0.343 in its equivalent logarithmic form.

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Video Transcript

Express 0.7 cubed equals 0.343 in its equivalent logarithmic form.

So, what we’ve got in the question is exponential form. And as we’re asked to do, we want to change this into the equivalent logarithmic form. But how are we going to do this? Well, if we have an exponential form in the form 𝑏 to power of 𝑦 equals 𝑥 and we want to change it into logarithmic form, then what we’re going to get is log to the base 𝑏 of 𝑥 is equal to 𝑦. So, we can see this is how we change it between our two forms. So now, let’s use this to change what we have in our question.

So, we start off, as we said, in our exponential form. And we’ve got 0.7 cubed. So, our 0.7 is gonna be our 𝑏, and our three is going to be our 𝑦. And this is equal to 0.343. Well, the 0.343 is gonna be our 𝑥. Well now, if we express it into our logarithmic form, what we’re gonna have is log to the base 0.7 of 0.343 is equal to three. And that’s because, as we said, the 0.7 is our 𝑏, the 0.343 is our 𝑥, and the three is our 𝑦.

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