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Evaluate
Evaluate the function and show a step by step of this please

Evaluate Evaluate the function and show a step by step of this please-example-1
User Kineolyan
by
8.1k points

1 Answer

3 votes

Answer:

-43/102

Explanation:

You want the value of the given expression involving radicals and logs.

Rules

The relevant rules of logarithms and radicals are ...


\log_b{(b^a)}=a\\\\\sqrt[n]{a^m}=a^{(m)/(n)}

Application

The given expression can be simplified as follows.


\frac{\log_3{\sqrt{243\sqrt{81\sqrt[3]{3}}}}}{\log_2{\sqrt[4]{64}}+\log{10^(-10)}}=\frac{\log_3{(3^5\cdot(3^4\cdot3^{(1)/(3)})^{(1)/(2)})^{(1)/(2)}}}{\log_2{2^{(6)/(4)}}+(-10)}\\\\\\=\frac{\log_3{3^((5+13/6)(1/2))}}{3/2-10}=(43/12)/(-17/2)=-(2\cdot43)/(12\cdot17)=\boxed{-(43)/(102)}

A suitable calculator can give you the same result.

Evaluate Evaluate the function and show a step by step of this please-example-1
User Stefano Cremona
by
8.2k points

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