Question 189006
{{{ln((8e)^4)}}} Start with the given expression.



{{{4*ln(8e)}}} Pull down the exponent using the identity {{{ln(x^y)=y*ln(x))}}}



{{{4*(ln(8)+ln(e))}}} Break up the log using the identity  {{{ln(A*B)=ln(A)*ln(B)}}}



{{{4*(ln(8)+1)}}} Evaluate the natural log of "e" to get 1.



Note: since the natural log is really a log with base "e", this means that



{{{y=ln(e)}}} ---> {{{e^y=e}}} ----> {{{y=1}}}



{{{4*(2.0794+1)}}} Evaluate the natural log of 8 to get approximately 2.0794



{{{4*(3.0794)}}} Add



{{{12.3176}}} Multiply



{{{12.3}}} Round to the nearest tenth




So *[Tex \LARGE \ln\left(\left(8e\right)^{4}\right) \approx 12.3]