Question

Evaluate the log without a calculator ( Show your work )


`log_(2) \sqrt[5]{16}`

Answer 1

Answer: x = 1/5

//Hope it helps.

Answer 2

`\log_2(\sqrt[5]{16} )=(4)/(5)`

Explanation:

The given logarithmic expression is:

`\log_2(\sqrt[5]{16} )`

We rewrite the radical as an exponent to obtain;

`\log_2(\sqrt[5]{16} )=\log_2(16^{(1)/(5)} )`

Recall and use the power rule;
`\log_a(M^n)=n\log_a(M)`

`\log_2(\sqrt[5]{16} )=(1)/(5)\log_2(16 )`

We write 16 as an index number to base 2.

`\log_2(\sqrt[5]{16} )=(1)/(5)\log_2(2^4)`

We apply the power rule again;

`\log_2(\sqrt[5]{16} )=(4)/(5)\log_2(2)`

We simplify to get;

`\log_2(\sqrt[5]{16} )=(4)/(5)(1)`

`\log_2(\sqrt[5]{16} )=(4)/(5)`