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Convert log base 4 of 2 equals 1/2 into an exponential equation

2
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So logarithm literally tells you

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so if we were to just look at this part over here.

4
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A logarithm is just saying tell me the exponent

5
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that I would have to raise my base to

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that I would have to raise 4 to to get to 2.

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So tell me the exponent that I would have to raise it to, to get to 2.

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And so this equation written as a logarithmic equation

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says: I need to raise 4 to the 1/2 power in order to get 2.

10
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So if I wanted to write it as an exponential equation,

11
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I could literally just say: well if I raise 4, and that's this 4 right over here, that's my base,

12
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To this exponent, to the 1/2 power,

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then that is going to be equal to 2.

14
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And we're done. We've written the same equation as an exponential equation.

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The value of a logarithm, this is to think:

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What do I get if I raise 4 to the 1/2 power?

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I get 2 if I raise 4 to the 1/2 power.

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This is saying: What power do I have to raise 4 to to get to 2?

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And then that is equal to 1/2.

20
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So logarithm is saying: What power do I have to raise the base to

21
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to get what's inside the logarithm.

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This says: what do I get to when I raise 4 to the 1/2 power.