Can log_2(x) be expressed as a series?

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The discussion confirms that the logarithm of an arbitrary base, such as log_2(x), can indeed be expressed as a series. This is achieved by utilizing the relationship log_b(x) = ln(x)/ln(b), where ln denotes the natural logarithm. The participants emphasize that this conversion allows for the application of series expansion techniques to logarithmic functions. The clarity of this mathematical relationship facilitates further exploration of logarithmic series representations.

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geor
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Hello all,

I am aware that we can write ln(x) as a series.
But what can we say for a logarithm of an arbitrary base?

Can we write for example log_2(x) as series?

Thanks in advance..
 
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Remember that the logarithm in base b of a number is just a constant multiple of the natural logarithm of the number, specifically: logb(x) = ln(x)/ln(b).
 
Oh yes, of course! Thanks a lot..
 

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