Respuesta :

Setor9
64^x=16^x-1====> Make the bases the same
4^3(x)=4^2(x-1)=> Solve for x by bringing down the exponent without the base.
3(x)=2(x-1)=====> Distribute
3x=2x-2======> Now solve for x
3x = 2x-2
-2x  -2x
x=-2
Therefore x is negative two
adioabiola

To solve for x in 64^x = 16^x−1 yields; x = -2

By the laws of indices where;

(a⁵)² = a⁷

We can rewrite the expression 64^x = 16^x−1. as follows;

  • (4³)^x = (4²)^(x-1)

In essence;

  • 4^(3x) = 4^(2x-2)

Since both sides of the equation have equal indices base. we can conclude that;

  • 3x = 2x - 2

  • 3x - 2x = -2

x = -2

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