Question

Solve 64^x = 16^x-1

Please help I need to find what x equals

Answer 1

x = -1

Explanation:

lhs is 64 to the power of something, while rhs is 16 to the power of something. so x cannot be a positive number.

if you keep x as 0, 64^0 > 16^-1, which means 1 > 1/16. hence x should be lesser than 0.

With -1, 64^-1 = 16^-2, 1/64 = 1/64

Answer 2

x= -2

Explanation:

64^x = 16^x-1

64= 4^3 and 16=4^2

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

so we now cancel the 4 from both sides and equate the powers

3x=2(x-1)

3x=2x-2

we now put all the x on one side

3x-2x=-2

x= -2