Video: Converting an Equation from Logarithmic to Exponential Form

Express logβ‚‚ 4 = 2 in its equivalent exponential form.

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Video Transcript

Express log base two of four equals two in its equivalent exponential form.

This equation log base two of four equals two is said to be in a logarithmic form because it involves a logarithm. For the general equation log base π‘Ž of 𝑏 equals 𝑐, which is in logarithmic form, the equivalent exponential form is π‘Ž to the power 𝑐 equals 𝑏.

These two forms are stating the same relationship between the numbers π‘Ž, 𝑏, and 𝑐. What are the values of π‘Ž, 𝑏, and 𝑐 in this problem? To write our equation in exponential form, we find the values of π‘Ž, 𝑏, and 𝑐 and substitute them in.

π‘Ž equals two. 𝑏 equals four. And 𝑐 equals two. That’s all there is to it. The equation that log base two of four equals two, which is in logarithmic form, expresses the same information as two to the power two equals four, which we know to be true.

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