SOLUTION: Express {{{e^(log(4,x))}}} as a power of x.

Question 304781: Express as a power of x.

Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!
Express as a power of x.


Use the change of base formula, where NEW and OLD refer to the
NEW and OLD bases:



We want to use that to change  from OLD base 4 
to NEW base e:



And we realize that  is the same as 

So

 

And therefore



becomes



We write that quotient exponent  as a product 



Now we use the rule 



Next we use the rule  to write the above as



and that is a power of x.

Edwin

RELATED QUESTIONS
Please help me express {{{e^log(4,x)}}} as a power of... (answered by themathtutor2009)

pre calculus express as a sum ( log 1ooo to a power over b to the 2 power) 2. 2log A... (answered by Boreal)

4) Express as a single logarithm with a coefficient of 1:... (answered by jim_thompson5910)

Express as a single logarithm with a coefficient of 1:... (answered by lwsshak3)

Express the following product of powers of x as a single power of x : x �x^4 � x^2 (answered by stanbon)

Express as a single log rhythm: {{{log( x^3 +8 ) - log( x^2 -2y + 4 ) + log (x-2)}}} (answered by stanbon)

express as a single logarithm 5 log x - 3 log y + 4 log... (answered by josmiceli)

Express as a single logarithm: log x + log 1 � 4 log... (answered by fractalier)

What is half of {{{ 4^(x+3) }}} ? Express as a power without... (answered by josgarithmetic)