Question

See equation.

Answer 1

\[1/4=64^{2x-1}\]

Answer 2

64 = \(4^3\), agree?

Answer 3

you can use ln

Answer 4

yes

Answer 5

\(\Large \color{MidnightBlue}{\Rightarrow 64^{2x - 1} = (4^{3})^{2x - 1} = 4^{6x - 3} }\)

And

\(\Large \color{MidnightBlue}{\Rightarrow {1 \over 4} = 4^{-1} }\)

Now, as the bases are equal, then we can make an equation of the exponents.

\(\Large \color{MidnightBlue}{\Rightarrow 6x - 3 = -1 }\)
\(\Large \color{MidnightBlue}{\Rightarrow 6x = 2 }\)
\(\Large \color{MidnightBlue}{\Rightarrow x = {2 \over 6} = {1 \over 3}}\)