Question

What is the value of `\log _ { 10} root3 10`?

Answer 1

`log_10\root[3]{10} = log_10 (10)^{1/3} = 1/3`

Answer 2

`1/3`

Use the property of logarithm that state `log_bx^n=nlog_bx` and the power fraction identitity `root(n)x^m=x^(m/n)`

See below

Explanation:

`log_10root(3)10=log_10(10^(1/3))=1/3log_10 10=1/3`

Because `Log_10 10=1`