Question

Solve for x in the exponential equation below and check your solution.642x-1 = 164x-3

Answer 1

We have this exponential equation here:

`64^(2x-1)=16^(4x-3)`

Let's create equivalent expressions with the same base, 2.

`2^(6(2x-1))=2^(4(4x-3))`

Since they have equal bases we can set the exponents equal to each other.

`6(2x-1)=4(4x-3)`

Simplify the equation.

`12x-6=16x-12`

Solve for x.

`\begin{gathered} 6=4x \\ x=(6)/(4)=(3)/(2) \end{gathered}`

The answer is x = 3/2.