Quick question.
How would you simplify : $$2^{Log_4(x)}$$
Thank ya!
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Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – Martin R Oct 24 '20 at 19:45
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$log_a(x) = \frac{\log x}{\log a}$ and $a^x = e^{\log(a)x}$ – achille hui Oct 24 '20 at 19:46
2 Answers
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Rearrange $$ 2^{\log_4x} = (4^{1/2})^{\log_4(x)} = 4^{1/2\log_4x} = 4^{\log_{4}x^{1/2}} = x^{1/2}. $$ Take your time to make sure you understand the rule of indices/logarithms applied in each equality.
DanLewis3264
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$$2^{\log_4(x)} = 2^{\frac{\log_2(x)}{2}} = \sqrt{x}$$
TheSilverDoe
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Very helpful thank you. I misapplied the change of base, this clears it up nicely. – Thomas Hegarty Oct 24 '20 at 21:24