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#
