Question 614702
<pre>
Simplify: Log(base 4)64^x

If {{{log (4, (64^x))}}}, then read on!!
{{{log (4, (4^3)^x)}}}
{{{log (4, (4^(3x)))}}}
       <font color = red><font size = 4><b>3x ----- Applying {{{log (a, (a^b))}}} = b
<u>OR</font></font></b></u>

Let simplified form, be t
{{{log (4, (64^x))}}}
{{{4^t = 64^x}}} ----- Converting to EXPONENTIAL form
{{{4^t = (4^3)^x}}} 
{{{4^t = 4^(3x)}}}
Exponents are equal, if BASES are equal, and so, <font color = red><font size = 4><b>simplified form</font></font></b></u>, or t = <font color = red><font size = 4><b>3x</font></font></b></u></pre>