Question Video: Solving Exponential Equations in Logarithmic Form Mathematics

If 3^(π‘₯) = 24, what is the value of π‘₯?

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Video Transcript

If three raised to the power π‘₯ is equal to 24, what is the value of π‘₯?

To find the value of π‘₯, we’re going to use the fact that for 𝑏, 𝑛, and π‘š greater than zero, the expression 𝑏 raised to the power 𝑛 is equal to π‘š is equivalent to the logarithm to the base 𝑏 of π‘š is equal to 𝑛. Comparing with the given expression that is three raised to the power π‘₯ is equal to 24, we have 𝑏 equal to three, 𝑛 is equal to the π‘₯ in our expression, and π‘š is equal to 24.

If we now put these values into the logarithmic expression, we have the logarithm to the base three of 24 is equal to π‘₯. And hence, if three raised to the power π‘₯ is equal to 24, then π‘₯ is equal to the logarithm to the base three of 24.

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