`1/2^x = 5/8^(x+3)` `` Solve for x. 

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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`1/2^x = 5/8^(x+3)`

`==> 8= 2^3`

`==> 1/2^x= 5/2^(3(x+3))`

`==> 1/2^x = 5/2^(3x+9)`

`==> 2^(3x+9)= 5(2^x)`

`==> 2^(3x)(2^9) = 5(2^x)`

`==> 2^(3x)/2^x = 5/2^9`

`==> 2^(2x) = 5/2^9`

`==> log 2^(2x) = log (5/2^9)`

`==> 2x log 2 = log 5 - log 2^9`

`==> 2x = (log5 - 9log2)/log2 `

`==> 2x = log5/log2 - 9`

`==> x = log5/(2log2) - 9/2~~-3.34`

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