<PRE><B>Question 444093</B>
{{{ln(sqrt(e))}}}
you know that you can write the square root as an exponent
{{{ln(e^(1/2))}}}
Write the log equiv of exponents:
{{{(1/2)*ln(e)}}}
you know the ln of e = 1
{{{(1/2)*1}}} = {{{1/2}}}
:
log{{{sqrt(2)(4)}}}, Assume this means the log base{{{sqrt(2)}}} of 4?
:
remember the log of the number is equal to exponent of the base
using common logs as an example, log,base10(1000) = 10^3, log is 3
:
In this problem, what exponent of {{{sqrt(2)}}} is 4
2 * 2 = 4, therefore
{{{sqrt(2)}}}*{{{sqrt(2)}}}*{{{sqrt(2)}}}*{{{sqrt(2)}}} = 4
or we can say {{{sqrt((2))^4}}} = 4
therefore
log{{{sqrt(2)(4)}}} = 4?</PRE>