T Torri0016 New member Joined May 15, 2011 Messages 1 May 15, 2011 #1 Which of the following is equivalent to log base 4 of 64^x? 1.) 4^3x 2.) 3^x 3.) 4x 4.) .25x 5.) 3x
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 May 15, 2011 #2 Rewrite your log: \(\displaystyle log_{4}(4^{3})^{x}\).........[1] \(\displaystyle log_{4}4^{3x}\)..........[2] Log property, \(\displaystyle log(a^{b})=b\cdot log(a):\) So, [2] is equivalent to: \(\displaystyle 3x\cdot log_{4}4\) Now, see it?.
Rewrite your log: \(\displaystyle log_{4}(4^{3})^{x}\).........[1] \(\displaystyle log_{4}4^{3x}\)..........[2] Log property, \(\displaystyle log(a^{b})=b\cdot log(a):\) So, [2] is equivalent to: \(\displaystyle 3x\cdot log_{4}4\) Now, see it?.
