Answer:
![x=\frac{7}{12}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7%7D%7B12%7D)
Step-by-step explanation:
We have been given an equation:
![\frac{1}{16}=64^{4x-3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D%3D64%5E%7B4x-3%7D)
In order to solve this equation we will convert the base same on both sides of equation:
we can write
we get:
![\frac{1}{4^2}={4^3]^{4x-3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%5E2%7D%3D%7B4%5E3%5D%5E%7B4x-3%7D)
Now, using ![\frac{1}{x^n}=x^{-n}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%5En%7D%3Dx%5E%7B-n%7D)
Here, n is 3 and x is 4 on l;eft hand side of the above equation:
![4^{-2}=4^{3\cdot (4x-3)}](https://tex.z-dn.net/?f=4%5E%7B-2%7D%3D4%5E%7B3%5Ccdot%20%284x-3%29%7D)
![4^{-2}=4^{12x-9}](https://tex.z-dn.net/?f=4%5E%7B-2%7D%3D4%5E%7B12x-9%7D)
We can equate the powers when base are same
Hence, 12x-9=-2
Now, we will solve for x we get:
12x=7
![x=\frac{7}{12}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7%7D%7B12%7D)