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

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

Guest Feb 1, 2015

#1
+85726
+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:

#1
+85726
+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
#2
+92206
+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

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