1/4x=4^10+x?

Answer 1

Please use parantheses to make clear what you mean; is the left side 1/(4 x) or (1/4) x?

If it is the first one, use the property of the equation that it can be multiplied on both sides with the same number (non-zero); thus, multiply with 4x, then group terms.

If it is the second, substract from both sides (1/4)x, then substract 4^10, and find x.

Answer 2

Here is what you wrote:
1/4x=4^10+x
x/4 = 4^10 +x
x/4 - x =4^10
-3x/4 =4^10
-3x = 4^11
x = - (1/3)(4^11)

But maybe you meant:
1/(4x) = 4^(10+x)
log1 -log 4x = (10+x)log 4
-log4x = 10log4+xlog4
-log4 -logx = 10log4 +logx +log4
-2logx = 12log4
logx = -6log4 =log 4^-6
x = 4^-6 = 1/4^6

But maybe you meant something else. Please write what you mean using parentheses and braces and brackets as required to make your question completely unambiguous.