+0  
 
0
233
2
avatar

(1/64)^x = 1/512 what is x?

Guest Feb 1, 2015

Best Answer 

 #1
avatar+80987 
+13

1/64 = 1/2^6    1/512 = 1/2^9   ..so we have..

(1/2^6)^x  = (1/2)^9 =

(1/2)^(6x) = (1/2)^9      we have like bases, so equating exponents, we have

6x =9   divide by 6

x = 9/6 = 3/2

 

 

CPhill  Feb 1, 2015
Sort: 

2+0 Answers

 #1
avatar+80987 
+13
Best Answer

1/64 = 1/2^6    1/512 = 1/2^9   ..so we have..

(1/2^6)^x  = (1/2)^9 =

(1/2)^(6x) = (1/2)^9      we have like bases, so equating exponents, we have

6x =9   divide by 6

x = 9/6 = 3/2

 

 

CPhill  Feb 1, 2015
 #2
avatar+91451 
+8

$$\\(1/64)^x = 1/512 \\
$turn both sides upside down and you get $
64^x=512\\\\
$method 1$\\
64^x=512\\
log64^x=log512\\
xlog64=log512\\
x=\frac{log512}{log64}\\
x=1.5\\\\
$method2$\\
64^x=512\\
64=2^6\quad and \quad 512=2^8\\
(2^6)^x=2^9\\
2^{6x}=2^9\\
6x=9\\
x=9/6=1.5$$

Melody  Feb 2, 2015

20 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details