Question

How do you find the exact value of `log_2 root4 8`?

Answer 1

`3/4`

Explanation:

`"using the "color(blue)"law of logarithms"`

`•color(white)(x)log_bx=nhArrx=b^n`

`rArrlog_2(root(4)(8))=n`

`rArrroot(4)(8)=2^n`

`"using the "color(blue)"law of exponents"`

`•color(white)(x)a^(m/n)=root(n)(a^m)`

`rArrroot(4)(2^3)=2^(3/4)=2^n`

`"since the bases on both sides are 2 we can equate"`
`"the exponents"`

`rArrn=3/4`

`rArrlog_2root(4)(8)=3/4`