Solve for x: 4^2x-1=10^1-x?

Brackets MUST be used or else question becomes nonsense.
Should be shown as :-
4^(2x - 1) = 10^(1 - x)
(2x - 1) log 4 = (1 - x) log 10
(2x - 1) (0.602) = 1 - x
2.204 x = 1.602
x = 0.727

Steps a million. rewrite the numerator interior the 1st term as (5x - a million) / [(x + a million) ( x- a million)] 2. rewrite the denominator of the 1st words as (x-5) / [(x-a million) (x-3)] 3. the 1st term reduces to [ (5x - a million) (x-3) ] / [ (x + a million) (x - 5)] 4. distinctive this by potential of the reciprocal of the 2nd term the cubic area is (x+a million) (x -5) (x-5) 5. the expresion will cut back to (x - 3) (x - 5) = 3 x^2 - 8x + 15 = 3 x^2 - 8x + 12 = 0 (x - 6) (x - 2) = 0 x = 2 or 6

1.89...

4^(2x - 1) = 10^(1 - x)
log[4^(2x - 1)] = log[10^(1 - x)]
(2x - 1)log(4) = (1 - x)log(10)
(2x)log(4) - log(4) = 1 - x
(2x)log(4) + x = 1 + log(4)
x[2log(4) + 1] = 1 + log(4)
x = [1 + log(4)]/[2log(4) + 1]

add your exponents. 40^x should be your final answer