Video: Changing the Subject of an Exponential Equation

Make π‘₯ the subject of the equation 𝑦 = 2^(π‘Žπ‘₯ + 𝑏), assuming that π‘Ž β‰  0.

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Video Transcript

Make π‘₯ the subject of the equation 𝑦 equals two to the π‘Žπ‘₯ plus 𝑏 power, assuming that π‘Ž does not equal zero.

We can go from exponential form to logarithmic form, π‘Ž to the π‘₯ power equals 𝑏. So taking our equation and using the same circle method, two to the π‘Žπ‘₯ plus 𝑏 equals 𝑦. Now let’s solve for π‘₯. Let’s subtract 𝑏 and then divide by π‘Ž. So we’ve subtracted 𝑏 and now divide both sides by π‘Ž.

Therefore, log base two of 𝑦 minus 𝑏 divided by π‘Ž is equal to π‘₯.

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