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

##### 1 Answer

Oct 1, 2017

#### 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#