Question Video: Solving Exponential Equations in Logarithmic Form Mathematics

Video Transcript

If three raised to the power 𝑥 is equal to 24, what is the value of 𝑥?

To find the value of 𝑥, we’re going to use the fact that for 𝑏, 𝑛, and 𝑚 greater than zero, the expression 𝑏 raised to the power 𝑛 is equal to 𝑚 is equivalent to the logarithm to the base 𝑏 of 𝑚 is equal to 𝑛. Comparing with the given expression that is three raised to the power 𝑥 is equal to 24, we have 𝑏 equal to three, 𝑛 is equal to the 𝑥 in our expression, and 𝑚 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 𝑥. And hence, if three raised to the power 𝑥 is equal to 24, then 𝑥 is equal to the logarithm to the base three of 24.