Question

Solve for x. Show your work.
4^5x-4 = 64^2x+12

Answer 1

Answer: x =-40

Step-by-step explanation: simplify 64 to have the same bottom number as the other side : 4

this way you can set the exponents equal to each other

4x4x4 =64

so 64 = 4^3

4^5x-4 = 4^3(2x+12)

set exponents = to each other

5x-4=3(2x+12)

5x-4=6x+36

-5x both sides

-4=x+36

-36 both sides

-40=x

x=-40

check by plugging in x

hope that helps

Answer 2

No solution

Explanation:

We can solve for x using algebraic manipulation, exponent rules, and logarithmic functions.

`4^(5x)-4 = 64^(2x)+12`

↓ rewrite 64 as 4³

`4^(5x)-4 = 4^(3(2x))+12`

↓ simplify

`4^(5x)-4 = 4^(6x)+12`

↓ subtract 12 from both sides

`4^(5x)-16 = 4^(6x)`

↓ substitute a variable (a) for
`4^x`.

`a^(5)-16 = a^(6)`

↓ move all the a's to one side

`0 = a^(6) - a^(5) + 16`

Now we can see that there is no solution for a, and by extension, for x.