Question

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

Answer 1

-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.