Question

Solve the exponential equation 1/16=64^4x-3

Answer 1

$\frac{1}{16} = 64^{4x-3} , \frac{1}{4^2} =( (4)^3)^{4x-3}, 4^{-2} =(4)^{3(4x-3)}, -2=3(4x-3)$,$-2=12x-9, 12x=-2+9=7, x= \frac{7}{12}$

Answer 2

Answer:

$x=\frac{7}{12}$

Step-by-step explanation:

We have been given an equation:

$\frac{1}{16}=64^{4x-3}$

In order to solve this equation we will convert the base same on both sides of equation:

we can write $16\text{as}4^2\text{and}64\text{as}4^3$ we get:

$\frac{1}{4^2}={4^3]^{4x-3}$

Now, using $\frac{1}{x^n}=x^{-n}$

Here, n is 3 and x is 4 on l;eft hand side of the above equation:

$4^{-2}=4^{3\cdot (4x-3)}$

$4^{-2}=4^{12x-9}$

We can equate the powers when base are same

Hence, 12x-9=-2

Now, we will solve for x we get:

12x=7

$x=\frac{7}{12}$