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# C3 Logs - how does this simplify to (2x)^2? watch

1. How does e^2ln(2x) simplify to (2x)^2? I don't understand it.

Thanks
2. (Original post by vector12)

How does e^2ln(2x) simplify to (2x)^2? I don't understand it.

Thanks
Either so

or notice that using log laws.
3. Well, 2ln(2x) is equivalent to ln(2x)^2 (one of the log rules) and since ln is the inverse of e^x, e^lnx can cancel out to x.
4. (Original post by vector12)

How does e^2ln(2x) simplify to (2x)^2? I don't understand it.

Thanks
2Ln(2x) = Ln[(2x)^2]. I assume you know understand that e^Ln(a) = a.
5. (Original post by _gcx)
Either so

or notice that using log laws.
Wouldn't it be this instead? I thought the power moves up only to be the power of the power, rather than the power of the whole thing.
so
6. (Original post by vector12)
Wouldn't it be this instead? I thought the power moves up only to be the power of the power, rather than the power of the whole thing.
so
No,

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