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

 Feb 1, 2015

Best Answer 

 #1
avatar+94526 
+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

 

 

 Feb 1, 2015
 #1
avatar+94526 
+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+95177 
+8

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

.
 Feb 2, 2015

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