`4^(2x-5)=64^(3x)` Solve the equation.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

To evaluate the given equation `4^(2x-5)=64^(3x)` , we may let `64 =4^3` .

The equation becomes:  `4^(2x-5)=(4^3)^(3x)` .

Apply Law of exponents: `(x^n)^m = x^(n*m)` .



Apply the theorem: If `b^x=b^y` then `x=y` .

If `4^(2x-5)=4^(9x` ) then `2x-5=9x` .

Subtract 2x on both sides of the equation `2x-5=9x` .



Divide both sides by `7` .


`x = -5/7`

Checking: Plug-in `x=-5/7` on `4^(2x-5)=64^(3x).`






`4^((-45)/7)=4^((-45)/7)`  TRUE


`0.000135~~0.000135`  TRUE

Thus, the `x=-5/7`  is the real exact solution of the equation `4^(2x-5)=64^(3x)` .

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial